The sign for rodeo looks like you are twirling a lasso above your head a couple times (as if getting ready to rope a calf).
RODEO or "Twirl lasso":Hold your hand up above or to the side of your head and move your arm in a circle twice as if twirling a lasso.
RODEO: Version 2
Another version of this sign initializes the handshape with an "R" hand. I suppose this could be helpful if your sentence were something to the effect of "At the rodeo the cowboy twirled his lasso." (Thus you would be able to use the initialized RODEO sign to specifically mean "rodeo" and use the more general sign to mean "twirl a lasso.")
Notes: