You could say "Att äta surströmming gör mig törstig." (To eat feremented herring makes me thirsty.) but it wouldn't work without the infinitive mark (att). I would personally say "Jag blir törstig av att äta surströmming." (I get thirsty by eating ferremented herring.)
However... now it sounds more like, it makes me thirsty to eat surströmming. Like.. it is part of another sentence. For example, doing something makes you thirsty to eat surströmming. So it doesn't mean the same thing.