We report the detection and characterization of a new magnetospheric star, HD 135348, based on photometric and spectropolarimetric observations. The TESS light curve of this star exhibited variations consistent with stars known to possess rigidly rotating magnetospheres (RRMs), so we obtained spectropolarimetric observations using the Robert Stobie Spectrograph (RSS) on the South African Large Telescope (SALT) at four different rotational phases. From these observations, we calculated the longitudinal magnetic field of the star <B z >, as well as the Alfvén and Kepler radii, and deduced that this star contains a centrifugal magnetosphere. However, an archival spectrum does not exhibit the characteristic "double-horned" emission profile for Hα and the Brackett series that has been observed in many other RRM stars. This could be due to the insufficient rotational phase coverage of the available set of observations, as the spectra of these stars significantly vary with the star's rotation. Our analysis underscores the use of TESS in photometrically identifying magnetic star candidates for spectropolarimetric follow-up using ground-based instruments. We are evaluating the implementation of a machine-learning classifier to search for more examples of RRM stars in TESS data.