Must I Learn Thai to Move to Thailand?

Dependig on where you're living in Thailand, it may  be necessary to learn Thai. If moving to the Sukumvit neighbourhood of Bangkok and associating with mainly expats and teaching English, than no, you don't absolutely have to learn Thai - though you'll want to. If moving to a rural Thai in the North, than yes, you'll probably need to learn the language.

Learning Thai can be difficult especially for Western speakers - the language is tonal - meaning that every syllable has a tone associated with it, which effects the meaning of the word. Thus two words can be spelled exactly the same, but mean drastically different things. This can definitely be confusing, but to familiarize yourself with a few basics there's a great primer here - "Learning the Thai Language".