It usually means that the person is in a very awkward or bad situation, often by some action (or inaction) on their own part.
"I slept late and missed the test. I'm so screwed!"
If a person has been cheeted or treated badly, the more likely way to say it would be:
"I have been screwed!"
It seems like a small difference, but there is definitely a difference in how the two statements would be understood.