Yes, you can, and native speakers certainly do:
BOY SCOUTS, VOLUNTEERS RAISE FOOD DONATIONS FOR HOLIDAYS
Another common expression is to collect food, (non-monetary) donations, or relief supplies for some charitable effort, as in the above article:
Dozens of people are helping regional Ulster and Greene County Food Banks to collect food for Thanksgiving and Christmas.
Still, the expression "raise food donations" is not uncommon, at least in headlines:
Pair of holiday events will raise food donations for the less fortunate
Lincoln students raise food donations for needy families
Local mayors battle to raise food donations for locals in need
However, the text of the article uses "collect" rather than "raise":
Two mayors with the same goal of providing for families in need will have a friendly competition next week to see who can collect the most donations.
Note that it's "raise food donations" and not just "raise food", since that means "to grow food plants", or "raise animals for food."