A pivot door hinge assembly includes a clamp housing, wedge, and base plate. The clamp housing is preferably generally U-shaped and has an interior channel. The interior channel is tapered such that one end of the interior channel is wider than a second end. The wedge is located in the interior channel of the clamp housing and in between one side of the glass door and an inner surface of the clamp housing. The wedge is also tapered. The set screw is located at one end of the clamp housing and is used to urge the wedge from that end toward the other end. As the wedge moves away from the wider end of the interior channel, this causes the wedge to move closer to the glass door and apply greater pressure against the glass door and an interior side of the clamp housing. This is because the tapered interior channel forces the wedge away from one side of the clamp housing toward the other side. A base plate having a raised portion may also be used. The raised portion extends at least slightly above a surface of the base plate and mates with a recessed portion of a clamp housing.