In order to overcome the inherent latency in multi-user unmanned aerial vehicle (UAV) networks with orthogonal multiple access (OMA). In this paper, we investigate the UAV enabled uplink non-orthogonal multiple access (NOMA) network, where a UAV is deployed to collect the messages transmitted by ground users. In order to maximize the sum rate of all users and to meet the quality of service (QoS) requirement, we formulate an optimization problem, in which the UAV deployment position and the power control are jointly optimized. This problem is non-convex and some variables are binary, and thus it is a typical NP hard problem. In this paper, an iterative algorithm is proposed with the assistance of successive convex approximate (SCA) technique and the penalty function method. In order to reduce the high computational complexity of the iterative algorithm, a low complexity approximation algorithm is then proposed, which can achieve a similar performance compared to the iterative algorithm. Compared with OMA scheme and conventional NOMA scheme, numerical results show that our proposed algorithms can efficiently improve the sum rate.