Statistical modeling of random networks has been a widely used approach to uncovering interaction mechanisms of complex systems and predicting unobserved links in real-world networks. In many applications, network connections are collected via egocentric sampling: a subset of nodes was sampled first, after which all links involving this subset of nodes were recorded; all other information was missing. Compared with the typical assumption of uniformly missing at random, the egocentrically sampled partial networks requires specially designed modeling strategies. The previous available statistical methods are either computationally infeasible or based on intuitive designs without theoretical justification. We propose a method to fit general low-rank models for egocentrically sampled networks, which include several popular network models. The method is based on spectral properties and is computationally efficient for large-scale networks. The proposed method gives a consistent recovery of the missing subnetwork due to egocentric sampling for sparse networks. To our knowledge, this is the first available theoretical guarantee for egocentric partial network estimation in the scope of low-rank models. We evaluate the method on several synthetic and real-world networks and show that it delivers competitive performance in link prediction tasks.