Grounding rod for detached garage?
...And you didn't put a concrete-encased conductor (UFER ground) in the slab? Sigh. That's the easy way out and the most effective ground you can make in most places.

Yes, you need a grounding electrode (ground rod) local to the detached building. Connecting to reinforcing steel in the slab would have provided a very good grounding electrode, but if it's already poured, that ship has sailed.

6 AWG solid is the default minimum size for a connector to a grounding electrode. 8 AWG might be acceptable given that the feed size is 10 AWG, but I'm having trouble tracking down the exact language where that is mentioned. It's one of the messier (or more confusing) sections of the code (IMHO.)