You can't once you deleted your private key file and if you don't have a copy of it then you have no way of logging in. You can try this assuming it's an EBS backed instance:
- Stop your EC2 instance
- Detach your root Volume (/dev/sda1) -- Assuming this is
Volume A
- Spin up a new EC2 instance of the same type.
- Attach
Volume A
to that new instance as/dev/sdf
- ssh connect to his new instance.
mkdir -p /mnt/xvdf
mount /dev/xvdf /mnt/xvdf
- `cp ~/.ssh to /mnt/xvdf/home//.
chmod 700 /mnt/xvdf/home/<username>
chmod 600 /mnt/xvdf/home/<username>/authorized_keys
- Shutdown new instance
- Detach
Volume A
on new instance - Reattach
Volume A
on /dev/sda1 on original instance. - Start original instance.
You should be able to login now.