There is a simple factual response based on the fossil record, "No. Dinosaurs and people did not coexist" but this does not really answer the question "did humans draw dinosaurs?" -- with the implicit assumption that the two coexisted. Here I will provide some commentary about cave drawings (petroglyph, pictogram) with sources for further reading.
First a warning.
Mythologies created by rock art researchers and archaeologists are not limited to invented unlikely meanings, they also include vast numbers of “likely explanations”. Unfortunately, plausibility of interpretations does not render them any more credible, in fact from the epistemological perspective the unlikely versions are preferable: they are easier to refute. 
The above quote talks about created mythologies, but the warning applies to other subjective interpretation, such as "what does this image represent?"
One common such interpretation is that ancient humans have created representations of dinosaurs found in petroglyphs. However, these interpretations are wrong. Common explanations are local wildlife (such as a giraffe), or artistic liberties or human-animal hybrids. For instance, this paper (abstract) outlines several famous cases:
To support claims of the coexistence of humans with dinosaurs and pterosaurs, young-earth creationist authors have identified several pieces of ancient rock art as depictions of dinosaurs or pterosaurs. Here, nine such claims are investigated. An alleged pterosaur painting in Black Dragon Canyon, Utah, is actually not a single painting. Its "head" and "neck" are a painting of a person with outstretched arms. Its torso and limbs are those of a painting of a second person with outstretched arms, whose body continues into the "pterosaur's" "wing." The other "wing" is a painting of a horned serpent. The three paintings only appear connected because someone outlined the group with chalk. An alleged dinosaur petroglyph in Havasupai Canyon, Arizona, is a stylized bird with an extension on one foot; the hooked line that represents its head and neck is a stylized bird head. A second alleged dinosaur petroglyph in Havasupai Canyon is a stylized bighorn sheep or rabbit. An alleged dinosaur cave painting in Tanzania is an obvious giraffe. Three alleged cave paintings of long-necked dinosaurs in Zambia have short necks and most likely represent lizards. An alleged dinosaur painting on Agawa Rock in Lake Superior Provincial Park, Ottawa, represents Underwater Panther, a supernatural lake guardian of Ojibwe tradition. An alleged pterosaur painting at Alton, Illinois, is the product of the imagination of a nineteenth-century American author. These pieces of rock art now join the ever-growing pile of discredited "evidence" for the ancient coexistence of humans and dinosaurs. 
A similar article (by the same author as  that repeats many of the same examples of ) also expands on other critical failings of identification, such as a "mastodon" being incorrectly identified and another instance of a mastodon in a cave painting less than 100 years old.  Despite the many examples of incorrect attribution and misidentification, there is some sense in which this question is legitimate, which is some mythical reconstruction of available evidence by prehistoric man.
In several historic locations, the existence of fossil footprints was deemed to be of special significance to historic hominins, significant enough to be recorded (for example, ). In some cases, the fossil was reproduced in petroglyph, and there is at least one instance where a mythological creature was reconstructed from footprints, for instance:
(taken from .) The petroglyphs are reported favorably in , and  as a reconstruction from the tridactyl footprints; a mythical creature called "//Khwai-hemm" that, at the time of the story telling, only its tracks remained (i.e., the fossil footprints). A similar mythological construction near a similar footprint is identified in 
There is no fossil evidence humans and dinosaurs co-existed (see other answers). The cave paintings given as evidence to support that claim are either 1) clearly misidentified (vocabulary word of the day: Pareidolia ) or 2) a mythological construction based on local folk lore.
 Bednarik, Robert G. Myths about Rock Art. Journal of Literature and Art Studies, ISSN 2159-5836. August 2013, Vol. 3, No. 8, 482-500 https://s3.amazonaws.com/academia.edu.documents/35548236/Myths_rock_art.pdf?AWSAccessKeyId=AKIAIWOWYYGZ2Y53UL3A&Expires=1546964986&Signature=0db0PSp1CoTsZEGMS65Sixt%2BK7o%3D&response-content-disposition=inline%3B%20filename%3DMyths_About_Rock_Art.pdf
 Senter, Phil. 2012. More "dinosaur" and "pterosaur" rock art that isn’t. Palaeontologia Electronica Vol. 15, Issue 2;22A,14p;
 Bednarik, Robert G. Pleistocene Palaeoart of the Americas. Arts 2014, 3, 190-206; doi:10.3390/arts3020190 https://www.mdpi.com/2076-0752/3/2/190/pdf
 Ellenberger et al. Bushmen Cave Paintings of Ornithopod Dinosaurs: Paleolithic Trackers Interpret Early Jurassic Footprints. Ichnos, 12:3, 223-226, DOI: 10.1080/10420940591008971 https://doi.org/10.1080/10420940591008971
 Lockley et al. An introduction to thunderbird footprints at the Flag Point pictograph-track site: preliminary observations on Lower Jurassic theropod tracks from the Vermillion Cliffs area, southwestern Utah. Part of The Triassic-Jurassic Terrestrial Transition 2006 Bulletin 37 pp310-314. http://econtent.unm.edu/cdm/ref/collection/bulletins/id/265
 Gerard D. Gierlinski and Konrad Z. Kowalski. Footprint of an large, Early Jurassic ornithischian from the ancient sacred site of Kontrewers, Poland. Part of The Triassic-Jurassic Terrestrial Transition 2006 Bulletin 37 pp217-220. http://econtent.unm.edu/cdm/ref/collection/bulletins/id/265