Is there a Centaur race in Pathfinder? If so, please leave a link. If not how do I get around constructing one?
Yes, from the Advanced Race Guide
The Pathfinder RPG: Advanced Race Guide splatbook features expanded rules on modifying and creating races, and includes a playable Centaur race as one of the examples - as can be seen here in the Pathfinder SRD. (Unhelpfully, you will need to refer to rules on this page to figure out all the Centaur's actual properties - the trait "Quadruped", for instance, actually increases the creature's speed by 10 feet, which combines with the independently selected Fast quality (another +10ft), to give this Centaur race a final movement speed of 50ft.)
The ARG qualifies the power level of these new races using "race points" (RP). It is worth noting that the Centaur, as a 29 RP race, is explicitly at the very high end as far as racial power levels go, and it is considerably more powerful than the standard races (which mostly reverse-engineer to 10 or less RP). The Sidebar: Challenging Advanced and Monstrous Races on this page has some advice on how to try balance for a party which includes such more powerful races. The page also offers the following advice in its introductory section:
In addition, these rules allow you to create powerful races meant to take on more challenging encounters than those typically faced by the core races. You can create new races, model a race after an existing monster, or even “power up” core races in order to play those races side-by-side with more powerful new races.
If you want to allow very powerful races like Centaurs, you could also allow the rest of the party to use the ARG rules to add new traits and features to core races to "catch up" to the more powerful race (though the options available aren't stunningly well-balanced, so you should probably retain a veto to prevent egregious minmaxing). You can always simply judge that these particular individuals are extremely unusual examples of their respective race, and leave the rest of the world unaffected.
Alternatively, you could tone down the centaur by removing some of its buffs, so it's not quite so powerful compared to other races. The +2 "Advanced X" trait it has for all physical abilities costs a total of 12RP, so dropping those puts it at a more reasonable 17RP, comparable to other "advanced" races like Tieflings (13RP) and Aasimar (15RP). This approach is probably a lot easier to balance.