I'm a data scientist but my degree is in political science. Overall, political science is a healthy mix of qualitative and quantitative research. However, almost all political scientists will pick a broad research methodology and stick with in. The field has, over the past three decades, made huge strides in quantitative research and has transitioned almost entirely to statistics-backed efforts. There are exceptions. Programs outside of the US tend to be less quantitative. Some programs withing the US are still heavily qualitative or all formal modeling (as opposed to statistical modeling). But the top journals are almost all dominated by papers with strong statistical components.

Within the quant side of polisci, the field is at the cutting edge of observational research (as opposed to experimental). Therefore, regression analysis of various types dominates. Some of the best and most clever work is also done by identifying natural experiments, cleverly designing actual experiments, and using state-of-the-art techniques for causal inference (matching, instrumental variables, regression discontinuity, etc...).

In fact, there is an entire sub-discipline of political science called political methodology. Some excellent methodologists doing cutting-edge work (in applied statistics) include Kosuke Imai, Michael Ward, Gary King, Phil Tetlock, and Kristian Gleditsch among many many more.