I have a 7 year old son and a 10 year old daughter. Is there a law in Oregon about having them share a bedroom?

There are no laws. If you are in HUD/sect 8 housing they have rules.
You need to be careful and watch for things that give you reason to believe they should no longer share a room.
Your daughter is getting to the age she should have her own room soon.

I agree, there are no laws saying they can't share. However they will get to an age where each will need their own personal space, for different reasons. Girls need privacy for periods, bras, panties and such girly things, boys need privacy for nakked girl pictures, masturbation, and other such boy things.

They aren't quite at that age yet so you should be OK, however keep it in mind and as nohelp said, watch for signs of puberty and maturing to decide when its time.

Most apartment complexes require you to have 2 kids or less to a room unless they are infants or toddlers. And as nohelp said, seciton 8/hud has their own rules as well.