On 1 April 2006, the Taitung earthquake (Mw 6.1) occurred in Taiwan at the boundary between the Philippine Sea and Eurasian plates, where high convergence rates contributed to the development of Plio‐Pleistocene orogeny in the region. From the joint inversion of seismic and geodetic data, we identified the event’s fault geometry and reconstructed the distribution of coseismic fault slip. We modeled fault geometries with increasing complexity and selected the model that best reproduced all datasets, simultaneously. Even though the earthquake magnitude was moderate, rupturing occurred in two steps. The initial rupture was generated on a listric, north–south‐trending fault (for which dip decreases with increasing depth), and was immediately followed by movement along a perpendicular structure that cross‐cuts the main fault at 5 km south of the earthquake hypocenter. The average slip along the rupture was 30 cm, with a maximum of 87 cm. Oblique‐reverse fault movement was characterized by a predominant left‐lateral component. The amount of slip is well constrained for offsets of more than 5 cm, with an associated uncertainty of 32%. For slip amounts greater than 5 cm, uncertainties on rake and rupture time are 11° and 0.54 s, respectively. The rupture propagated from the hypocenter bilaterally, moving slightly faster toward the south (2.5±0.4 km/s) than to the north (1.7±0.1 km/s). To the south, the rupture was rapidly transmitted upward at the junction with the cross‐cutting east–west segment, whereas in the north, the rupture remained confined to the lower segment of the main fault. From Global Positioning Systems (GPS) and seismic data (time window <1 min), we infer that the cross‐cutting segment was activated following coseismic rupture on the main north–south fault, yet close enough in time to be associated with coseismic movement acquired by GPS (daily solutions).