It is! (in the early 2d games) To save on cartridge space, Link only had sprites made facing one direction. When facing the other direction, the sprite was simply flipped. The manual had a lore blurb about a superstition regarding keeping your shield facing Death Mountain to handwave it.

Starting with Ocarina of Time, Link was given a (mostly) consistent handedness, typically being left-handed but sometimes doing a few things, like archery, right-handed.

The Wii version of Twilight Princess flipped the entire game, including the character models, left to right, making Link a righty to make the motion controls more intuitive for most players. Skyward Sword was then built with a right-handed Link for the same reason.

With Breath of the Wild, Link was made right-handed despite the game not using motion controls for swordplay. The top-down games have kept Link as a lefty, though.