It did not rain very often when Chuck Norris was a kid.
Why?
Because his favorite childhood song was "Rain Rain Go Away."
Listen here, you snowflake! The joke is that Chuck Norris is so tough and powerful that even as a child, his favorite song had the power to stop the rain. This is a play on the trope that Chuck Norris is an invincible dude who controls everything. You're probably the type who cries when it drizzles, aren't you?