User identity linkage, which aims to link identities of a natural person across different social platforms, has attracted increasing research interest recently. Existing approaches usually first embed the identities as deterministic vectors in a shared latent space, and then learn a classifier based on the available annotations. However, the formation and characteristics of real-world social platforms are full of uncertainties, which makes these deterministic embedding based methods sub-optimal. In addition, it is intractable to collect sufficient linkage annotations due to the tremendous gaps between different platforms. Semi-supervised models utilize the unlabeled data to help capture the intrinsic data distribution, which are more promising in practical usage. However, the existing semi-supervised linkage methods heavily rely on the heuristically defined similarity measurements to incorporate the innate closeness between labeled and unlabeled samples. Such manually designed assumptions may not be consistent with the actual linkage signals and further introduce the noises. To address the mentioned limitations, in this paper we propose a novel Noise-aware Semi-supervised Variational User Identity Linkage (NSVUIL) model. Specifically, we first propose a novel supervised linkage module to incorporate the available annotations. Each social identity is represented by a Gaussian distribution in the Wasserstein space to simultaneously preserve the fine-grained social profiles and model the uncertainty of identities. Then, a noise-aware self-learning module is designed to faithfully augment the few available annotations, which is capable of filtering noises from the pseudo-labels generated by the supervised module.