Agree with pp, our city has 2 opportunities for 3 yos. Instructional classes, often parent/child or else the scrimmage/games only format where the kids just play "games" for one hour each week.
We've done both types before and like both for different reasons and for different kids. I usually wait until mine are older (4.5 years), but am also considering singing up my 3yo who loves to play soccer.
We're opting for the scrimmage/games program (its intramural, totally non-competitive, no one keeps score) because he loves to play (and wants a team jersey) but isn't into drills or learning the finer points of the game. I think it will be enough to have fun and understand the basic 3: kick the ball into the net to score, pass to teammates, stay inside the white lines. He can learn all of that in the games only format. The instructional classes involved practice passing, dribbling around cones, and different types of kicks. It would all go over my 3yos head.
We've found one program with a set schedule (all 3 yo teams play at 9 am, 5 yo play at 10 am, etc.). They do exist but you'll have to search for it. Most of them changes times/fields each week and its a royal PITA, imo.
Ds1 (2006). Ds2 (2010). Ds3 (2012).