regionmask itself is a pure Python package, but its dependencies are not. The easiest way to get them installed is to use conda. The package is available on the conda-forge channel.
conda install -c conda-forge regionmask cartopy
All required dependencies can be installed with pip. You can thus install regionmask regionmask directly:
pip install regionmask
Note, however, that the optional dependency cartopy can be very difficult to install with pip.