Q: What is the legal age to babysit in Oregon state?

A: I don't know if there is a specific law on this but here are some links that lead me to believe that age 14 or older might be safe:

This article says you can't leave a child 10 or younger alone - so that age or younger would not qualify to babysit.

http://www.oregonlegalresearch.com/content/when-can-i-leave-my-kids-home-alone

This article says that children age 14 can work but only limited hours! So this may interfere with some baby sitting jobs;

http://www.oregon.gov/BOLI/WHD/CLU/Pages/W_CLU_Taminors.aspx

Q. How many hours may minors work in a day?

A. There are no limits on the number of hours 16- and 17-year-olds may work in a day. However, 14- and 15-year-olds may not work during school hours, may not work more than three hours on any school day, and may not work more than eight hours on non-school days. Also, 14- and 15-year-olds may only work between the hours of 7:00 a.m. and 7:00 p.m. (and as late as 9:00 p.m. between June 1 and Labor Day).

Q. How many hours may minors work in a week?

A. Sixteen- and 17-year-olds may work up to 44 hours per week. Fourteen- and 15-year-olds may work at most 18 hours per week during the school year and 40 hours per week when school is not in session.

I would add to this that there is an element of common sense. You would not want to leave a child in the care of another minor - no matter what that minor's age is, if you know that for whatever reason, the minor you want as a baby sitter is not mature enough and responsible enough to keep your child safe and secure. I believe you could still be charge with negligence and child endangerment if you ignore obvious signs.