is this correct?

This is not common and would not not sound natural in American English, though it would be understood. If "shift" were to be used, it would more likely be accompanied by a prepositional phrase ("Could you shift to the left") but it still wouldn't be common. Many other phrases would be more typical in such a situation, such as:

slide over
slide down
move over
move down

My impression is that "could you shift" is college slang.

Thank you Noddy and Valpower.

college slang ? in where? UK or USA?

I've heard it used both places, more frequently in the UK.