Have a file named ~ (tilde) in my home-directory

I just noticed that I have a file called ~ in my ~-directory.

$ ls -la ~
...
-rw-r-----  1 x1 x1  733962240 Mar  1 17:55 ~
...

Any idea how I can mv or rm it?

The pretty much ultimate solution when it comes to files that can't be deleted by normal means:

ls -il 

The first column will show the inode number of the files.

find . -inum [inode-number] -exec rm -i {} \;

This will delete the file with the specified inode-number after verification.

You should be able to refer to that file as ~/~ (without quotes) because tilde-expansion only applies the the tilde (~) at the very beginning of the word.