Knowing from :help ale-python-pylint that we want to adjust g:ale_python_pylint_options to include --rcfile, I would drop
let g:ale_python_pylint_options = '--rcfile '.<filename>
in wherever the right place is for you. That could be wherever you configure ALE, if a single setting is right; or, it could be in an ftplugin (use b:…) if you need to change the name based on the specific file/project/whatever.
For the specific ~/.vim/.pylintrc, you should be able to do
let g:ale_python_pylint_options = '--rcfile '.expand('~/.vim/.pylintrc')
It's possible expand() isn't necessary if pylint will properly tilde-expand its arguments, but I haven't tested that (a smoke-test would be to run something like sh -c 'pylint --rcfile '\''~/.vim/.pylintrc'\'' <other options>' and see if it picks up your settings; run it in your own shell if single-quotes disable all expansion: pylint --rcfile '~/.vim/pylintrc' <other options>).