We present a staircase-shaped transmissive metasurface for linear-to-circular (LTC) polarization conversion, achieving an axial ratio bandwidth (ARBW) of about 41% and covering the entire X band (8-12 GHz). Unlike designs based on discrete resonators, the proposed structure is based on meander-line conductive elements with electrical continuity across unit cells. This promotes distributed surface currents that contribute to a broader operational bandwidth. The metasurface operates in transmission mode and enables switching between right- and left-handed circular polarization (RHCP/LHCP) through a simple 90 degrees mechanical rotation. In addition, the LTC response remains robust under oblique incidence, with the ARBW remaining above 33% for incidence angles up to 45 degrees. Experimental results are in very good agreement with simulations and confirm stable handedness switching. Owing to its geometrical nature, the operating frequency can be easily scaled by adjusting the unit-cell dimensions. As a proof of concept, a Ku-band (12-18 GHz) design achieving comparable broadband performance is also demonstrated. These results highlight the potential of continuous, distributed-current-based metasurfaces for compact and broadband polarization control in microwave systems.