"Can you give me a piece of paper?"
把 structure should be accepted, it is more correct as you are asking for a transfer. 你可以把一张纸给我吗？
Actually 把字句【把 structure】and 被字句【被structure】can be changed into each other. For example： 你可以把纸给我吗
这张纸可以被给我吗 【Can this paper be given to me？】 BUT the latter is quite weird for Chinese natives......
This is a common phenomenon in Chinese sentence. Just remember this structure. When you use oral Chinese, you can use this structure. 你 is added to make this sentence more formal.