OK, no, they don't actually consume food through their eyes. That would be a bit too bizarre. However, they do use their eyeballs to help push food down their throat.
A brief article about this crazy behaviour was published in Cosmos magazine recently, and it sums up the facts quite nicely:
"For the northern leopard frog (Rana pipiens), eyes are not only good to see prey with, they're good for swallowing it too. This contortionist of the animal world can retract its eyes into its head, and move them down towards its throat. The frog still uses its tongue to swallow, but the eyes offer a useful helping hand."
Don't try this at home, people. We are not frogs.
Quote source: Cosmos magazine, Issue 28 (Aug/Sept 2009), p.14