When playing the Romans, I used those El Cheapo throwaway skirmishers (Light Auxilia by that point). With that funky +4 bonus they get against chariots and elephants an outer layer of those guys generally mired the chariots quite well enough for the legionaires to charge in and reduce them into matchsticks.

Failing that (or having run out of disposable skirmishers), a deep formation of stationary legionaires generally seemed to absorb the charge well enough. Sure, the formation went to Hell, but actual casualties tended to be light and once the chariots stop moving they're pretty much goners.

I actually found the Pharaoh's Bowmen to be a bigger pain than the Chariot Archers. Auxilia Archers outrange the CAs, but cannot hit the PBs who're making pincushions out of the first-line units (aka "melee wall") without moving to a relatively unprotected forward position.

I usually resolved the matter by sending a few packs of Warhounds to occupy the guys with funny bows. The mutts normally got slaughtered, of course, but by the time they were all down I'd usually done something dreadful to the rest of the Egyptian horde. The doggies didn't seem to work very well on the chariots, by the way.