Look in Boots or other chemist, they sell supports for everything including wrist. Are you on any medication for the problem, if not there are gels such as Voltarol and also anti-inflamatory pills such as ibruprofen.
You could also try arthritis gloves, which gently compress your hand to provide relief from pain. I'll give you this link as an example
http://tinyurl.com/z78ect3
but it might be better to obtain them from a pharmacy (in order to ensure that you get the correct size).
Just a point, splints hold the wrist rigid so therefore shouldn't be used continuously as this will make the joint even more stiff which in turn makes the arthritis worse. The gloves are a good option or the wraparound supports which still allow movement.
I have arthritis (moderately severe) in my left wrist - following a broken bone.
Supports are OK, but I now see a specialist for a steroid injection into the joint. It is painful at the time (when the anaesthetic wears off) but the last time gave me 6 months pain-free wrist movement and I think that this is worth the few days discomfort. Perhaps that is the way to go?