Yes, eating carrots can help your eyesight. But it's not a cure-all.

Popular Science 

Yes, eating carrots can help your eyesight. The World War II propaganda that touted the veggie wasn't totally wrong, but carrots still won't give you night vision. Carrots' beta-carotene pigment can help support retina health, but the root vegetable still has its limits. Breakthroughs, discoveries, and DIY tips sent six days a week. In a British propaganda poster from World War II, an illustration in shadowy tones captures a dramatic nighttime scene: a woman and young girl peer around a black automobile, as if looking for a quick escape.