In D&D 3.5, the rule book says nothing about a Druid being able to tame or have a velociraptor. Could a Druid tame one and use it as his/her companion?
Yes, a Druid can have a dinosaur as an animal companion, but with some limitations according to the rules-as-written. A higher-level Druid has more options than just the basic list, as described in the alternative animal companions list. Starting at level 7, a Druid can choose a deinonychus as an animal companion.
But wait, you say, I'm asking about a velociraptor!
Yes, well, there's a funny story behind what we call "velociraptor." A "velociraptor" as they're popularly known is actually deinonychus. The movie Jurassic Park called them "velociraptor" because it's a cooler name, and people have been mixing them up ever since. Velociraptor was actually very small—about the size of a chicken—and not nearly as impressive as deinonychus.
This point is important, because D&D 3.5e calls them by their correct name, "deinonychus". And that precise dinosaur is a rules-as-written legal animal companion choice for a Druid of level 7 or greater. (Other dinosaurs are also on the list at higher levels.)
The caveat here is that the base companion starts out more powerful, so it gets a level penalty in its animal-companion benefits: you count as 6 levels lower for calculating your deinonychus' companion stats, feats, etc.
Yes, dinosaurs are animals and a number of them appear as options for the druid’s Animal Companion, particularly in the Player’s Handbook, Monster Manual III (which has a dinosaur skull on the cover), and the Eberron Campaign Setting (in Eberron, dinosaurs roam the Talenta Plains and many species are domesticated by the halflings who live there).
Options for a “raptor-like” dinosaur Animal Companions:
Also worth noting that all dinosaurs have the Animal type, which means Handle Animal and Wild Empathy also work on them.