Whenever I get a job interview as a junior web developer, I am told that my technical competence is undeniable but I'm way too introverted to be hired, especially in web agencies.
Are there some other programming jobs in which being extroverted isn't a requirement? Or I should keep searching for the right company? I don't think I can change my personality.
Keep talking and meeting new people, get better at socializing. Being introverted just means you prefer not to have to socialize some (or most) of the time, it doesn't mean you have to be bad at talking to people.
Being able to socialize is a skill, not a personality. How much you like to do it is what determines if you're extroverted or introverted.