Both /gɛt/ and /gɪt/ show up in the Wiktionary. The etymology strongly suggests that the pronunciation /gɛt/ is older. What is the source of the pronunciation /gɪt/? Is it confined to certain regions?
It does not seem to be coming from a regular sound change, as nobody says /pɪt/ for /pet/. On the other hand, it does affect "forget" (at least for me).
Best Answer
The pronunciation of "get" is indeed a very regional thing. I believe the "prestige" pronunciation in the USA is "/gɛt/". However Southern American English shifts a lot of vowels up, including shifting "get" to /gɪt/. The related African-American Vernacular English has the same feature. That means the predominant accents in both the Southeast quarter of USA and in most of its larger urban areas uses /gɪt/.
It's even a bit more complicated than that though. My own accent (I believe a mixture of Midlands and Southern Midlands) pronounces the word slightly differently depending on where it appears in the phrase. If it's in the middle, it is more likely to be closer to "/gɛt/", while at the end, it's more like "/gɪt/".
For instance, when my kids were in daycare, a popular mantra from the daycare workers was:
"You get what you get, and you don't throw a fit."
The way this is pronounced, the two phrases rhyme. However, the two "get"s don't quite rhyme with each other.