Yes, anyone can run it and it is highly recommended to do so for any serious Bitcoiner because only a full node independently verifies transactions and - with the right configuration - contributes to Bitcoin network availability & security.
But to be realistic, while you certainly can run Bitcoin Core on a Raspberry Pi, you should be aware that the initial download and verification of the entire Bitcoin blockchain will take a lot of time (literally weeks on a slow computer like a Raspi). You also need a harddrive or flash storage with at the absolute minimum 200+ GB capacity. Better have a TB drive, because the blockchain grows every day.
So running Bitcoin Core is more fun on a bit more powerful computer - perfect if you have an older notebook for example. But of cause you can do the initial download of the blockchain on a faster computer and then copy the data over (or use the drive) to your Raspi.