Batman’s history with guns is complicated, but generally Batman simply doesn’t use guns. Occasionally this is a point of pride motivated by the way his parents were gunned down. To my knowledge this carried over to the live action Batman television show of the 1960s starring Adam West and Burt Ward.
When it came time to make toys based on that series, at least one manufacturer thought a Batman with a gun made perfect sense.
That is a Batman utility belt from 1966 manufactured by Ideal. It was sold at auction in March 2013 for almost $8,500. According to the text of the auction description,
Accompanying the belt is the original early version spring-loaded Bat-Gun, which sports a bat symbol stencil on its side, painted grips and a black plastic trigger (later versions sometimes had an orange trigger, unpainted grips and/or lacked the stenciled logo). Trace of lt. wear to the paint on the textured grips. Gun functions as designed.
What’s even weirder is the whole Bat-Luger look to the gun. Presumably that’s some toy gun that Ideal was already manufacturing that made it easy to just slap a bat symbol on and repackage.