We examine the conditions necessary to trigger tremor along the San Jacinto fault (SJF) near Anza, California, where previous studies suggest triggered tremor occurs, but observations are sparse. We investigate the stress required to trigger tremor using continuous broadband seismograms from 11 stations located near Anza, California. We examine 44 Mw≥7.4 teleseismic events between 2001 and 2011; these events occur at a wide range of back azimuths and hypocentral distances. In addition, we included one smaller‐magnitude, regional event, the 2009 Mw 6.5 Gulf of California earthquake, because it induced extremely high strains at Anza. We find the only episode of triggered tremor occurred during the 3 November 2002 Mw 7.8 Denali earthquake. The tremor episode lasted 300 s, was composed of 12 tremor bursts, and was located along SJF at the northwestern edge of the Anza gap at approximately 13 km depth. The tremor episode started at the Love‐wave arrival, when surface‐wave particle motions are primarily in the transverse direction. We find that the Denali earthquake induced the second highest stress (~35 kPa) among the 44 teleseismic events and 1 regional event. The dominant period of the Denali surface wave was 22.8 s, at the lower end of the range observed for all events (20–40 s), similar to periods shown to trigger tremor in other locations. The surface waves from the 2009 Mw 6.5 Gulf of California earthquake had the highest observed strain, yet a much shorter dominant period of 10 s and did not trigger tremor. This result suggests that not only the amplitude of the induced strain, but also the period of the incoming surface wave, may control triggering of tremors near Anza. In addition, we find that the transient‐shear stress (17–35 kPa) required to trigger tremor along the SJF at Anza is distinctly higher than what has been reported for the well‐studied San Andreas fault.