I will also add that the official California "F3 tornadoes" in the NOAA database are probably dubious; Grazulis lists no tornadoes on 8/16/1973 or 2/9/1978, and the fact that there's literally ZERO contemporary documentation of those events tells me that they were likely not even tornadoes, let alone ones of F3 intensity. California DOES have a handful of genuine F2/EF2 tornadoes however, with some of the more recent ones being the 5/22/2008 Perris and 5/25/2011 Oroville tornadoes.
If there's any candidate for a true California F3 tornado, the July 1911 El Centro storm could certainly be it, but there's simply too much uncertainty. The "storm of cyclonic violence" swept through El Centro's business district, killing two people and injuring many others. Homes and businesses were unroofed and others were "demolished"; buildings that collapsed entirely included a church, a warehouse and a mill among others. The storm lasted "only a few minutes", and debris was carried for at least two blocks.
Grazulis again lists no California tornadoes in July 1911, but there is at least some contemporary documentation including a
July 17 article from The Salt Lake Evening Telegram, and another from The San Bernardino Sun on July 27:
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July 1911 would have put this event at the peak of monsoon season, and while it is rare to occur, monsoonal thunderstorms in this region can and have been known to intensify into supercells. The "storm of cyclonic violence" wording, and the fact that the SB Sun article specifically calls the event a tornado does give credence to this storm being a true tornado, but without further evidence I can't make the call.
Whatever the case, there's no doubt that a violent storm, whether it was a true tornado, a downburst or simply very severe straight line thunderstorm winds, wreaked havoc on El Centro that day.