Yes. You have to complete a first sea tour to apply for the Aviation Warfare Transition (the program name at the Navy Personnel Command). Right now, fighters are taking transitions since the retention in the fighter community is not great. That is subject to change, however. To transition, there are a lot of factors at play. Your current community has to be able to and be okay with giving you up, the community you want has to be able and want to take you, your front office (CO/XO) has to be supportive, you have to have good FITREPs (evaluations), and a good reputation. Transitioning also can come with career consequences, but plenty of people have transitioned and have done quite well in the Navy.
In my short time in flight school, it has become quite apparent that every community has its pros/cons and its own place in the Navy. There aren't really any terrible deals. Plus, there have been more than a few people I have met that said "I did not want to fly this platform out of flight school, but I love it, it's the best thing in the Navy, and I wouldn't change a thing."