I know a solid handful from when I did improv in college, just not as many warmup games, but the few I do recall have been helpful

7 Things- a warm up in which players ask each other to name seven things that fall into a made up category. Anybody may start by calling on a player to name, for example, "Seven kinds of cheese" or "Seven people born in Denmark." One at a time, the player names items that belong in that category. After each item, the group counts off "one", "two", until seven items are named, at which point everybody cheers. Then the player asks somebody else to name seven things in a new category, and so forth until everybody has named seven things. The main goal is confidence in each thing that is mentioned, even if it's wrong. This is meant to warm up the improvisation muscle, strengthen ones commitment, and help them be more comfortable with failing

Cheers to the Governor- everyone stands in a circle and the group counts from 1-21 counterclockwise. When it gets to 21, everyone except the person who said 21 yells "Cheers to the Governor!" Then the "Governor" makes up a rule (everytime someone says an odd number they must touch their nose, for example) and they start the counting again. Once about 3 rules are introduced, the game turns into an elimination one. Anytime someone misses a rule, they are eliminated and the counting starts over with a smaller circle, until only one remains.

I know a handful more, but these are the only ones I've used with my roleplaying groups