Yes, Earth exerts a force on Mercury. According to Newton's law of universal gravitation, every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Therefore, Earth, having a significant mass, exerts a gravitational force on Mercury, although this force is much weaker compared to the gravitational force exerted by the Sun on Mercury due to their vast difference in masses and proximity.