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.")
You can learn American Sign Language (ASL) online at American Sign Language University ™
ASL resources by Lifeprint.com © Dr. William Vicars