The invention relates to the soybean variety designated 01063921. Provided by the invention are the seeds, plants and derivatives of the soybean variety 01063921. Also provided by the invention are tissue cultures of the soybean variety 01063921 and the plants regenerated therefrom. Still further provided by the invention are methods for producing soybean plants by crossing the soybean variety 01063921 with itself or another soybean variety and plants produced by such methods.