Archers are mentioned in Roman texts as belonging to Roman armies. In Caesar (BC 3.88-93) they are present on Pompey's side at Pharsalus, where he deploys them along with his cavalry and slingers. The Pompeian archers are effective against Caesar's cavalry, but Caesar orders his concealed 4th line to suddenly pounce on Pompey's cavalry and puts them to rout. Then Caesar's forces fall upon the archers and slingers and massacre them. Caesar says the archers and slingers, without cavalry cover, were left destituti inermes sine praesidio ('abandoned, defenseless, without protection'). It is pretty clear that the archers (and slingers and cavalry) are all auxilia units. not part of the legions. The preferred ranged combat method of the legionnaires was always the pilum, the medium-range javelin. It seems to have been very effective and perhaps had more 'shock and awe' value than an arrow. In this same category were the scorpiones, which shot very heavy bolts. The shock value of this weapon was incredible, and if you saw your friend(s) killed by one of those bolts, you generally lost your will to fight very quickly.

Archers also appear on Trajan's Column, on both sides of the fighting. There are a lot of different varieties, with most appearing to depict Syrian or Sarmatian types (their little conical helmets give them away). If you scroll down on this site, there are some pictures of archers from the column along with some discussion of the types.