How to make git not prompt for passphrase for ssh key on windows?

You can run this in git bash:

eval `ssh-agent -s`
ssh-add ~/.ssh/*_rsa

it will ask for pass phrase in the second command, and that's it. Each additional action you will need to do (which once required pass phrase) won't ask you for the pass phrase (see an example in the screen shot below):

A slightly better and permanent solution is to auto launch the ssh-agent when opening the git bash on windows. You can copy/paste the below in your .profile or .bashrc. I prefer to put it on the .profile

env=~/.ssh/agent.env

agent_load_env () { test -f "$env" && . "$env" >| /dev/null ; }

agent_start () {
    (umask 077; ssh-agent >| "$env")
    . "$env" >| /dev/null ; }

agent_load_env

# agent_run_state: 0=agent running w/ key; 1=agent w/o key; 2= agent not running
agent_run_state=$(ssh-add -l >| /dev/null 2>&1; echo $?)

if [ ! "$SSH_AUTH_SOCK" ] || [ $agent_run_state = 2 ]; then
    agent_start
    ssh-add
elif [ "$SSH_AUTH_SOCK" ] && [ $agent_run_state = 1 ]; then
    ssh-add
fi

unset env

This solution was taken from this github help article