Could an asteroid be large enough to become spherical due to its own gravity?
In principle an asteroid could become spherical.
The definitions of bodies have been changed. If a body orbits the sun and is spherical it is now classified as a dwarf planet.
Objects in the asteroid belt meet the first criteria. Most are not spherical and hence are called asteroids. Some bodies in the asteroid belt such as Ceres are spherical and were promoted to dwarf planet status.
Asteroids are not large enough to become spherical. However, asteroids can collide to form bigger bodies. It is possible that after a collision an asteroid can be large enough to become spherical under its own gravity.