Vehicle positioning using raw global navigation satellite system (GNSS) observations from smartphones is crucial for intelligent transportation and smart driving. However, it is challenging to achieve high accuracy due to GNSS signal blockage and reflection in urban areas. In this work, we propose a data-driven smartphone positioning system PhoeNix-RTK empowered by deep transformer model. PhoeNix-RTK corrects positions estimated by the real-time kinematic (RTK) approach by learning from GNSS features with PhoeNix model. To make latent features independent of satellites, PhoeNix encodes the GNSS features based on set transformer. To exploit the temporal dependence in the GNSS features, PhoeNix predicts correction vectors based on transformer in a sequence-to-sequence manner. Extensive experimental results on a public vehicle dataset demonstrate PhoeNix-RTK achieves high accuracy in urban areas, outperforming its counterparts.