Cellular networks have been successfully evolved over the decades. Especially, Long-Term Evolution (LTE) has been exceedingly successful and the security threats against LTE systems have increased rapidly. Particularly, tracking LTE user devices has been shown to be effective as the temporary user identifiers (IDs) are easily extracted and used to locate targeted devices by passive eavesdroppers. We notice that naive approaches, such as frequent updates of temporary user IDs, are insufficient to mitigate user-tracking attacks since the new and old temporary IDs for the same user device are easily linkable by adversaries who can measure the wireless channel characteristics between the user device and herself. In this paper, we propose an opportunistic uplink power control scheme to minimize the probability of successful user tracking by an adversary whose location is unknown. We devise the notion of average inference error probability in order to measure the level of users' location privacy. Moreover, we derive the closed-form expression of the approximated average inference error probability and formulate an optimization problem to maximize the average inference error probability under a constraint of an allowable power budget for each user. Against a passive adversary, our proposed power control scheme effectively degrades an adversary's inference ability by 50% when 10 users are scheduled in each transmission time slot, which will lead to almost 100% inference error at the adversary over multiple time slots.