Yes, we are taller in the morning.
From The transformation of spinal curvature into spinal deformity (2005):
The effects of gravity on the upright human posture are powerful:
Individuals are as much as 25 mm taller in the morning than in the
evening (1)(2), as a result of compressive forces bearing down all day,
And astronauts 'grow' by nearly 75 mm when released from the
force of the earth's gravity (3).
From NASA (2004):
Did you know that astronauts are up to 2 inches taller while they're in space? As soon as they come back to Earth, though, they return to their normal height.
To some degree, a similar stretching of the spine happens to you every night. When you lie down, gravity isn't pushing down on your vertebrae.
You can do your own experiments with a meterstick. Measure your height carefully as soon as you get up or while you are still lying down. You will find that you're about a centimeter or two taller.
That's not as much as astronauts change in space. The idea, however, is the same. As the day passes, your vertebrae compress through normal activities, and you'll lose those few centimeters you "grew" overnight.