Can A Raspberry pi mine bitcoin without an ASIC miner? I want to know if a raspberry pi can mine bitcoin without using an ASIC miner.
You certainly can compile a Bitcoin node on a Raspberry Pi, and it will act as a fullnode relaying transactions for the network.  For mining, while it probably would work technically, the chances of you ever mining a bitcoin are so low that its probably a waste of time.

You can run other coins based on PoS on a Raspberry Pi though and make money that way, I personally use Raspberry Pis as my Gridcoin and SolarCoin staking nodes.