Translation:If you were awake I would give you food.
As a native English speaker, "If you were awake (then) I'd give you food" with the contracted form of "I had" and an optional then is normal and fairly common.
But in written form I'd definitely include the "then".
Of course, "I would have given" works too but that would translate to "skulle jag ha gett dig", I believe.
As a native speaker who enjoys writing concisely I would remove then as superfluous.
This sentence has brought a question to mind: I would have given would be in the past while I would give is in the present. The latter case I could see myself saying where I actively talking to a sleeping pet, but not after the moment had past. So I wonder if Swedish uses the present conditional where English uses the past perfect.
So I wonder if Swedish uses the present conditional where English uses the past perfect.
No, this sentence is strictly in the present in Swedish too. It can only mean 'if you were awake (now), I would be giving you food (now)'. The person is talking to someone who is asleep. I blame it on the song I linked to in the top comment.