The Moon's rising point on the horizon shifts daily due to its orbital inclination and the season. For Tucson (32.2° N, 110.9° W), the azimuth typically ranges from ~60° (ENE) to ~120° (ESE) over a lunar month.
To find tonight's exact rise:
General pattern: Near full Moon, it rises near sunset in the E/SE. Near new Moon, it rises near sunrise in the E/NE. Weather and mountains (Santa Catalinas) may delay visibility.