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:
1st-level druids can have a leaellynasaura, which the Talenta halflings refer to as a fastieth. Eberron Campaign Setting
1st-level druids can also have the fictional swindlespitter, which is apparently a combination of the oviraptor, which it looks and acts like, and Jurassic Park’s inaccurate portrayal of the dilophosaurus, since it spits venom as that one did. Monster Manual III
4th-level druids can have an actual velociraptor, which the Talenta halflings refer to as a clawfoot. Note that the velociraptor was quite a lot smaller than most people imagine; Jurassic Park got it wrong. See deinonychus, below, as well as SevenSidedDie’s excellent answer. Eberron Campaign Setting
4th-level druids can also have the fictional fleshraker, which is called exactly that in Talenta. Frequently banned, as the fleshraker makes far and away the most powerful creature available as an Animal Companion (many attacks, Pounce, and a nasty poison on every attack). Monster Manual III
7th-level druids can have a deinonychus, which is what most people mean when they say velociraptor since the Jurassic Park “velociraptors” were actually deinonychus; the Talenta halflings call that one a carver. Player’s Handbook + Monster Manual
Also worth noting that all dinosaurs have the Animal type, which means Handle Animal and Wild Empathy also work on them.