Similarity joins are important operations with a broad range of applications. In this paper, we study the problem of vector similarity join size estimation (VSJ). It is a generalization of the previously studied set similarity join size estimation (SSJ) problem and can handle more interesting cases such as TF-IDF vectors. One of the key challenges in similarity join size estimation is that the join size can change dramatically depending on the input similarity threshold. We propose a sampling based algorithm that uses the Locality-Sensitive-Hashing (LSH) scheme. The proposed algorithm LSH-SS uses an LSH index to enable effective sampling even at high thresholds. We compare the proposed technique with random sampling and the state-of-the-art technique for SSJ (adapted to VSJ) and demonstrate LSH-SS offers more accurate estimates at both high and low similarity thresholds and small variance using real-world data sets.