I have a 12 week old kitten that only pees/poops once a day - I am now giving her water through a syringe to be sure she isn't dehydrated. When she does go, she uses the litter box and does go a lot. Is this normal?? She seems perfectly healthy but I've never had a kitten do this before.

Stop with syringe. She is only 12 weeks old which means a very small bladder. She will have to be encouraged to drink water, usually they play in it first, figuring out what it is. Always have water accessible to her. She will drink when she is thirsty. You are doing more harm then good trying to hydrate her.

Agreed, there is no need to syringe feed water, as long as she has access to water and is drinking she will be fine.
Also consider what you are feeding, if feeding canned food then she is getting liquid intake from that thus decreasing what she may drink normally.
Once a day urination is not concerning, as long as it is a good amount and she has a good stream.
If she tries to go but can't and makes multiple trips to the box with scant results then you have a reason to worry.
But you are risking aspiration if you continue to use the syringe.