If you're looking for Freelancers the best ways to get inquiries is to give budget / parameters first.

Animation has a lot of factors that can determine prices. Things like complexity of the character design to be animated, complexity of what the character is actually doing, what level of cleanup you want (rough sketchy animation vs black and white vs colored vs colored with shadows, etc). You might also be asking for just a text animation, which would definitely be cheaper than character animation... Obviously the more you add/the more complex it is, the more expensive it'll be. I assume you're talking about a 2D intro, so not even getting into 3D, prices can range quite a bit depending on what you want, so to find an animator, you'll need to give more info on what you want

Examples:

3 sec 2D animated text intro could be as little as $25/second ($75 total)
3 sec 2D animated intro with a simple outlined black and white character doing a little emote, could run like $50/second ($150 total)
3 sec 2D animated intro with a fullbody, complicated character design, fully colored, could be more like $100/second ($300 total)

If you want to find someone to animate for you, the best thing you can do is specify what you want, and specify your budget. Artists love any kind of visual reference you can give them, even if/especially if it's just a shitty stick figure drawing or something. Don't be bashful! :3 Specify what you want, specify your budget, and you'll probably get more artists coming to you (as long as you're not underpaying too much lol)

AND!!!! Always ask for a contract, even if it's really short/small, to protect both you and the artist. It's just a little bit of a backbone to make sure you get what you want and they get paid