Flash-Ponies

There is! Here are the four most common ways in increasing level of difficulty:
1. Become a super-great friend to an animator. So good, in fact, that he or she is willing to spend 5+ hours (depending on complexity and length) to animate your OC, when he or he could have instead worked on his own projects, watched amazing movies or TVs, hung out with friends, earned money at a normal job, or be going to school so he could get a job.
2. Pay an animator. Enough again, to offset the opportunity cost that he could be doing something else with that time.
3. Become famous! (Or be inspiring!) Like Ilovekimpossiblealot! Do something truly unique that involves your OC that your powers of persuasion is such you can verbally enslave animator(s) to animate your OC! (Although 3 is similar to 1, because you still need to be friendly enough that your powers of persuasion aren't detracted.)
4. Become an animator yourself and animate your own OC. Spend the time, effort, and money to get the proper tools and learn the skills you need for animating. Then spend that time to animate your OC!

There's also a less well-known option, that's somewhat similar to 2:
Buy out an animation company. Then you will have lots of peons bending to your very whim just to earn a livelihood! Muahahahahaha! Erm. Erhem. coughs

Seriously though. Animation takes a lot of work. Unlike something like voice-acting, where after you perfect your skills, the actual performance isn't so time-intensive, animation is probably more like carpentry. Where even if you learn a lot of skills that makes things look better for shorter amount of time, you still need to spend an egregious amount of time to put out a product. There's a reason for any sufficiently large animation project, the list of animators will always outstrip the list of voice actors. It takes a lot of work for very little.