Hold the bracket up on the brick wall to determine the height and position. While holding the bracket in place with one hand, use a pencil to mark the position of the holes.
Drill a pilot hole at the pencil marks. Use a masonry bit to drill the holes rather than a regular drill bit. Regular drill bits are not strong enough to drill through brick. Choose a spot in the brick rather than the mortar. Mortar is more likely to crumble and will be less sturdy than the brick.
Insert concrete or masonry anchors into the holes. Gently tap the anchors into place with a hammer.
Position your bracket over the holes so that the screw holes are directly over the anchors. Insert screws into the masonry holes and use a screwdriver to twist them into place.