Yes, based on modelling, the rotation of the Earth was slowed down by 0.06 microseconds per "day".
That is, a day would be made about one seventeen millionth of second longer than it otherwise would be if the dam had not been built.
Business Insider references NASA's Jet Propulsion Laboratory (JPL} - the original link is broken, but the JPL still make the claim in a 2005 press release:
Dr. Richard Gross of NASA's Jet Propulsion Laboratory, Pasadena, Calif., and Dr. Benjamin Fong Chao, of NASA's Goddard Space Flight Center, Greenbelt, Md., said all earthquakes have some affect on Earth's rotation. It's just they are usually barely noticeable.
To make a comparison about the mass that was shifted as a result of the earthquake, and how it affected the Earth, Chao compares it to the great Three-Gorge reservoir of China. If filled, the gorge would hold 40 cubic kilometers (10 trillion gallons) of water. That shift of mass would increase the length of day by only 0.06 microseconds and make the Earth only very slightly more round in the middle and flat on the top. It would shift the pole position by about two centimeters (0.8 inch).
In 1995, Dr Chao published a paper showing how to model the effects of major reservoirs on the moment of inertia (and the location of the poles):
That paper looked at 88 major reservoirs, not including Three-Gorges Dam - it wasn't opened yet.
In 2002, Dr Chao was a co-author of another paper:
In this paper, they use the same modelling from the 1995 paper to look at the effect of the Three-Gorges Dam.
when filled, the Three‐Gorges Reservoir would cause an overall change in Earth's dynamic oblateness J2 by +3.0 × 10−13, J3 by +2.4 × 10−12, and Earth's rotation by only +0.060 μs in length‐of‐day, but as much as 0.64 milliarcsecond in polar motion excitation toward the direction away from the longitude of the Three‐Gorges.
That a dam would affect the rotation of the Earth is not surprising. As the JPL article explains:
"Any worldly event that involves the movement of mass affects the Earth's rotation, from seasonal weather down to driving a car," Chao said.