Head-mounted Mixed Reality (MR) systems enable touch interaction on any physical surface. However, optical methods (i.e., with cameras on the headset) have difficulty in determining the touch contact accurately. We show that a finger ring with Inertial Measurement Unit (IMU) can substantially improve the accuracy of contact sensing from 84.74% to 98.61% (f1 score), with a low latency of 10 ms. We tested different ring wearing positions and tapping postures (e.g., with different fingers and parts). Results show that an IMU-based ring worn on the proximal phalanx of the index finger can accurately sense touch contact of most usable tapping postures. Participants preferred wearing a ring for better user experience. Our approach can be used in combination with the optical touch sensing to provide robust and low-latency contact detection.