Most tornado prediction is performed at a daily to sub-daily horizon and relies heavily on technology such as Doppler radar that can help identify convective storm formation. Although this prediction is certainly invaluable, in light of this year's anomalous and catastrophic tornado outbreaks in the United States, longer-horizon prediction of tornadoes may be useful for earlier preparation as well. It has been hypothesized that various climate oscillators may be related to United States tornado patterns. Although numerous studies have attempted to quantify relationships between tornado counts and climate oscillators, most have shown weak to moderate evidence of such associations. Here, we explore the relationship of the Southern Oscillation Index (SOI) with strong and violent United States tornadoes; a simple time series regression model shows visual and statistical evidence that the SOI may help in predicting annual out-of-sample tornado counts 1-3 years in advance. In addition, this model shows that the SOI may be particularly valuable in predicting highly anomalous tornado years. We caution that in recent years, the relationship seems to have grown weaker and that tornado database issues, including changes in operational definitions and the confounding effects of population change, complicate straightforward interpretation of this analysis. In addition, there is an apparent change point around the late 1970s, upon which the relationship between SOI and tornadoes seems to shift abruptly; this change point must be accounted for to yield predictive insights of SOI, but the physical and/or data-related explanation for the change point is not understood. Although the time series model developed in this work may serve as a useful starting point, visual exploratory analysis shows that the relationship appears to vary significantly over space and time. This may imply that, for such a long-horizon predictive model to truly be useful for disaster planning, the predictive model may need to be further improved and extended to a spatio-temporal model that also handles seasonality. In addition, physical explanation accompanying the data-derived insight on the SOI-tornado relationship would be valuable in advancing the understanding of climatological dynamics of tornadoes.