We present optical/near-infrared spectroscopy and photometry of the supernova (SN) PS15si. This object was originally identified as a Type IIn SN, but here we argue that it should be reclassified as a Type Ia SN with narrow hydrogen lines originating from interaction with circumstellar matter (CSM; i.e. SN Ia/IIn or SN Ia-CSM). Based on deep non-detections 27 d before discovery, we infer that this SN was discovered around or slightly before optical maximum, and we estimate the approximate time that it reached R-band maximum based on comparison with other SNe Ia/IIn. In terms of spectral morphology, we find that PS15si can be matched to a range of SN Ia spectral types, although SN 1991T-like SNe Ia provides the most self-consistent match. While this spectral classification agrees with analysis of most other SNe Ia/IIn, we find that the implied CSM-interaction luminosity is too low. We infer that the similarity between PS15si and the hot, overluminous, high-ionization spectrum of SN 1991T is a consequence of a spectrum that originates in ejecta layers that are heated by ultraviolet/X-ray radiation from CSM interaction. In addition, PS15si may have rebrightened over a short time-scale in the B and V bands around 85 d after discovery, perhaps indicating that the SN ejecta are interacting with a local enhancement in CSM produced by clumps or a shell at large radii.