Finger-gaiting manipulation is an important skill to achieve large-angle in-hand re-orientation of objects. However, achieving these gaits with arbitrary orientations of the hand is challenging due to the unstable nature of the task. In this work, we use model-free reinforcement learning (RL) to learn finger-gaiting only via precision grasps and demonstrate finger-gaiting for rotation about an axis purely using on-board proprioceptive and tactile feedback. To tackle the inherent instability of precision grasping, we propose the use of initial state distributions that enable effective exploration of the state space. Our method can learn finger-gaiting with significantly improved sample complexity than the state-of-the-art. The policies we obtain are robust and also transfer to novel objects.