To achieve this you need an SSH Client that is installed on your linux machine, a text editor like vim and your private key in openssh format.
Create a file in which to store your private key and edit it with vim to paste the key into it
vim examplekey.txt
When the editor starts press i to turn on insert mode.
Paste your key and save pressing ESC and typing :wq to write the file and return to commandline.
Afterwards change file permissons to 600
chmod 600 examplekey.txt
Now you can login to the linux remote server
ssh -i examplekey.txt root@remoteIP
When you are prompted to confirm the connection type yes and press enter.
That's it.