What hormone is responsible for controlling phototropism in plants?

The hormones responsible for phototropism are auxins.

Auxins are the phytohormone which is usually synthesised in the young tip of roots and shoots.

When the light falls on one side of the plant, auxin diffuses towards the shady side
of the shoot which stimulates the cells to grow longer, resulting in the bending of the shoot towards the light, thus auxin promotes phototropism.