The sign for "Frisbee" is ... well actually there is no sign for Frisbee.
At least you aren't likely to find such a sign in an ASL dictionary (other than this one).
I'm including the concept here though because I want you to learn how to "deal with uncertainty." Just because you don't know how to sign something doesn't mean you can't still have a signed conversation about it.
If you ask your Deaf buddy how to sign Frisbee he will likely tell you one of three things:
1. Spell it.2. Do a little movement that looks like you are throwing a Frisbee. Repeat.
3. Hold up curved-"L"-hands and show the size and shape of a Frisbee. (Which just happens to work well for the sign for "DISH." (Or any round flat object.)
Any of those approaches are fine. Number 3 -- holding up curved-"L"-hands -- isn't enough by itself but can be combined with the throwing movement and will thus be interpreted as a Frisbee. (Unless your wife is having one of those days and is throwing dishes - in which case the facial expression of the sign would be much more intense.)
Frisbee:
The double movement of the mime-like action helps to establish that you are signing a noun ("Frisbee" or "game of Frisbee") rather than a verb. If you wanted to sign the verb phrase "throw the Frisbee" (assuming that you've already established that you are talking about a Frisbee) you would simply mime the movement of throwing a Frisbee using a single, large movement.
Notes: