Angle adjustable bicycle rack assembly

A bicycle rack assembly includes a base plate (10) on the vehicle and has a first connection tube (11) to which a second connection tube (21) extending from a vertical portion of a frame (20) is connected. A slot (111) is defined in a wall of the first connection tube and a plurality of positioning holes (211) are defined through a wall of the second connection tube so that a first bolt (22) extends through one of the positioning holes and is engaged with the slot. Two support plates (25) are connected to a horizontal portion of the frame and each support plate has a first groove (251). A cap (26) has two second grooves (261) defined in an underside thereof and is connected to the horizontal portion with the two second grooves located to match with the first grooves so as to clamp two respective top tubes of bicycles in the grooves. The frame (20) can be adjusted an angle relative to the base plate (10).