You can. But it won't restore your older progress, nor it will save your current one—Facebook does not store game progress. Changing a Facebook account might come in handy if you linked the game to a FB account you don't use and want to change that.
To change the Facebook account your game is linked to:
- Open Facebook website or Facebook application;
- Go to 'Settings and Privacy';
- Select the 'Settings' section;
- Choose 'Apps and websites' under the 'Security' section;
- Find 'Logged in with Facebook' there;
- Remove War Robots from the list;
- Log out of Facebook account both in your browser and FB app on your device;
- Launch War Robots, go the the game menu and tap the Facebook button;
- Sign in with a Facebook account you'd like to link your game to.