Information provided by @Gord
As of September 2019 pywin32 is now available from PyPI and installs the latest version (currently version 224). This is done via the pip command
pip install pywin32
If you wish to get an older version the sourceforge link below would probably have the desired version, if not you can use the command, where xxx is the version you require, e.g. 224
pip install pywin32==xxx
This differs to the pip command below as that one uses pypiwin32 which currently installs an older (namely 223)
Browsing the docs I see no reason for these commands to work for all python3.x versions, I am unsure on python2.7 and below so you would have to try them and if they do not work then the solutions below will work.
Probably now undesirable solutions but certainly still valid as of September 2019
There is no version of specific version ofwin32api. You have to get the pywin32module which currently cannot be installed via pip. It is only available from this link at the moment.
https://sourceforge.net/projects/pywin32/files/pywin32/Build%20220/
The install does not take long and it pretty much all done for you. Just make sure to get the right version of it depending on your python version :)
EDIT
Since I posted my answer there are other alternatives to downloading the win32api module.
It is now available to download through pip using this command;
pip install pypiwin32
Also it can be installed from this GitHub repository as provided in comments by @Heath
