there is no linux port of warframe. there are two solutions to this problem: running it under steam's new proton/steamplay (with some unofficial patches/workarounds) or running it in a virtual machine. both can achieve stable gameplay, however in this guide we'll detail the more native steam option. please inform me if the instructions become outdated.
extract it and place all the files in your warframe installation, in the closest equivalent to /home/[user]/.steam/steam/steamapps/common/Warframe/Tools/ where [user] is your username
ensure a steam recognised controller is plugged in.
add the --firstrun launch option, but remove it after warframe opens up. you should now be set