McQueen is obviously in the living room at his Palm Springs home, practicing his aim before heading out for a shooting session in the desert. The date looks to be in the early 60s, 1963, unless I miss my guess, McQueen would have been 33 years old then. The pistol he's holding? Don't have a clue, not enough to go on.
Seriously though, looks like an H&R 940 to me as well.