Answer
Cathode rays were determined to have a negative charge because when a magnet was held near the ray, it was bent. This suggested that the ray had a negative charge because it was affected by the presence of a magnetic field.
Work Step by Step
Cathode rays consist of a vacuum tube with no air inside, a cathode, and an anode. When powered, there is a ray going from the anode to the cathode, and this ray could be deflected by a magnet, suggesting a charge. Additionally, the ray went from the anode to the cathode, and therefore the ray was negatively charged, since negatively charged particles flow from positive (anode) to negative (cathode).