Is it painful, or is it pumped? If it's painful, it might be an issue of flexibility/mobility or even tendonitis as well.
Try warming up your biceps for a moment with light weight, then do some stretching, prior to the squatting and see if that helps. You might even go as far as far as trying Voodoo floss from Rogue Fitness to help work out the bugs in your elbow/bicep tie in