Not as long as the game is implemented entirely on the client side. The "solution" is to implement the game rules and storage on the server side, and have the client be mostly UI, but this might be overkill for such a simple browser game.
You could make it harder by obfuscating the code, but that would only stop people who don't actually care.
If the game is deterministic you could keep a log of all game "events" and send that to the server, where the score would be calculated. This would make it more work to fake a score, but it would still be possible to fake, and it would also be a lot of work to build such a system.
$.ajax
or something similar in the browser console, without injecting any variable.