How far away was the litter box from the room she way playing in?
Make sure you are keeping the box very clean. Some cats like to pee and poo in different boxes.

Some people have good success with Dr Elsey's cat attract litter.
Make sure you clean the spot she used with an enymatic cleaner, or she'll just use that same spot again.

If she does a few more times, take her in to your vet to check for a urinary infection. If she has an infection, it hurts and she's trying to avoid the hurt by not using the box.

If you are new to cat ownership, I might suggest you do some reading. "Think like a Cat" by Pam Johnson-Bennett is a good one. (Can get through your library). Here is an article about litter boxes on her website:
Litter Box Problems Due to Location Aversion

 

Thanks for your reply. The litter box is in one bedroom while the kitten was down the hall and in the living room playing. I'm also thinking maybe it could of been her marking her territory since it is possible another animal urinated in that corner at one time. The carpet has recently been pulled up and it's just concret. She has been regularly using the litter box in her cage for a week. I am scooping their litter box daily, twice sometimes.

I'm going after work to get some enzyme cleaner. I am hoping it was just since she was young and too busy playing. Yep I've had cats for about 25 years now. Love them. Thanks for the link to the article too.