私の将来の夢は、プログラマーになることです。 を英語に訳すと？

My dream for the future is to become a software engineer. As a software engineer, I design inner workings of games, apps, and systems. I have this dream because I am interested in computer science. As a software engineer, I would like to create apps that all of you can use.

「プログラマー」は、職業的に「software engineer」とか「software developer 」の肩書きで呼ばれます。もし「プログラマー」という言葉を使いたければ、「computer programmer」に置き換えてください。