Yes, non-profits (501c3) can give scholarship grants.
On the 990EZ form where a non-profit would report income/expenses, one of the Expense lines is "Grants and Similar Amounts Paid". In the explanation of what that includes it says "Enter the amount of actual grants and similar amounts paid to individuals and organizations selected by the filing organization. Include scholarships, fellowship, and research grants to individuals."
I don't know the specific rules for what makes a grant "okay", but I suspect common sense will get you by - that you have stated criteria, objective decision factors, reasonable notification of the opportunity, etc. I noticed on the longer form (990), you have to include some additional informtion if an individual receiving the grant is in any way related to any key parties (like board members).
I sure hope so as our PTA has been funding a scholarship for about 22 years. It's in the name of a woman who was killed in a car accident while she was pres of the pta. Her 6 year old daughter was in the accident and survived and was awarded the scholarship when she graduated a few years back. I have to say there was not a dry eye in the house. I'm getting goosebumps just thinking about it!
After reading the thread on PTO's giving to non-profit, does anyone know if it is legal for a PTO to donate to a scholarship for a former student of the school? Many thanks!