There is no direct way to tell git which private key to use, because it relies on ssh for repository authentication. However, there are still a few ways to achieve your goal:
Option 1: ssh-agent
You can use ssh-agent to temporarily authorize your private key.
$ ssh-agent sh -c 'ssh-add ~/.ssh/id_rsa; git fetch user@host'
Option 2: GIT_SSH_COMMAND
Pass the ssh arguments by using the GIT_SSH_COMMAND environment variable (Git 2.3.0+).
$ GIT_SSH_COMMAND='ssh -i ~/.ssh/id_rsa -o UserKnownHostsFile=/dev/null -o StrictHostKeyChecking=no' \
git clone user@host
You can type this all on one line — ignore $ and leave out the \.
Option 3: GIT_SSH
Pass the ssh arguments by using the GIT_SSH environment variable to specify alternate ssh binary.
$ echo 'ssh -i ~/.ssh/id_rsa -o UserKnownHostsFile=/dev/null -o StrictHostKeyChecking=no $*' > ssh
$ chmod +x ssh
$ GIT_TRACE=1 GIT_SSH='./ssh' git clone user@host
Note: The above lines are shell (terminal) command lines which you should paste into your terminal. They will create a file named ssh, make it executable, and (indirectly) execute it.
Note: GIT_SSH is available since v0.99.4 (2005).
Option 4: ~/.ssh/config
Use the ~/.ssh/config file as suggested in other answers in order to specify the location of your private key, e.g.