The ornamental design for a mug with a rotatablecarabiner style handle, as shown and described.
FIG. 1 is an upper-front-left perspective view of a mug according to the present invention wherein the carabiner style handle is turned outward from the surface of the mug and the post on the carabiner style handle is locked in place by the hinge;
FIG. 2 is another upper-front-left perspective view of the mug of FIG. 1, wherein the carabiner style handle is turned to the side;
FIG. 3 is a left view of the mug of FIG. 1 wherein the carabiner style handle is turned outward, the right view being significantly reciprocal of the left view;
FIG. 4 is a front view of the mug of FIG. 1 wherein the carabiner style handle is turned outward;