Running SSH Agent when starting Git Bash on Windows

2013: In a git bash session, you can add a script to ~/.profile or ~/.bashrc (with ~ being usually set to %USERPROFILE%), in order for said session to launch automatically the ssh-agent.
If the file doesn’t exist, just create it.

This is what GitHub describes in “Working with SSH key passphrases“.

The “Auto-launching ssh-agent on Git for Windows” section of that article has a robust script that checks if the agent is running or not.
Below is just a snippet, see the GitHub article for the full solution.

# This is just a snippet. See the article above.
if ! agent_is_running; then
    agent_start
    ssh-add
elif ! agent_has_keys; then
    ssh-add
fi

Other Resources:

“Getting ssh-agent to work with git run from windows command shell” has a similar script, but I’d refer to the GitHub article above primarily, which is more robust and up to date.

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hardsetting adds in the comments (2018):

If you want to enter the passphrase the first time you need it, and not when opening a shell, the cleanest way to me is:

• removing the ssh-add from the .bash_profile, and
• adding “AddKeysToAgent yes” to your .ssh/config file (see “How to make ssh-agent automatically add the key on demand?“).

This way you don’t even have to remember running ssh-add.

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And Tao adds in the comments (2022):

It’s worth noting why this script makes particular sense in Windows, vs (for example) the more standard linuxey script noted by @JigneshGohel in another answer:

By not relying on the SSH_AGENT_PID at all, this script works across different msys & cygwin environments.
An agent can be started in msys2, and still used in git bash, as the SSH_AUTH_SOCK path can be reached in either environment.
The PID from one environment cannot be queried in the other, so a PID-based approach keeps resetting/creating new ssh-agent processes on each switch.