Purpose: Traditional BB-based geometric calibration methods for cone-beam CT (CBCT) rely strongly on foreknowledge of the scan trajectory shape. This is a hindrance to the implementation of variable trajectory CBCT systems, normally requiring a dedicated calibration phantom or software algorithm for every scan orbit of interest. A more flexible method of calibration is proposed here that accommodates multiple orbit types - including strongly noncircular trajectories - with a single phantom and software routine. Methods: The proposed method uses a calibration phantom consisting of multiple line-shaped wire segments. Geometric models relating the 3D line equations of the wires to the 2D line equations of their projections are used as the basis for system geometry estimation. This method was tested using a mobile C-arm CT system and comparisons were made to standard BB-based calibrations. Simulation studies were also conducted using a sinusoid-on-sphere orbit. Calibration performance was quantified in terms of Point Spread Function (PSF) width and back projection error. Visual image quality was assessed with respect to spatial resolution in trabecular bone in an anthropomorphic head phantom. Results: The wire-based calibration method performed equal to or better than BB-based calibrations in all evaluated metrics. For the sinusoidal scans, the method provided reliable calibration, validating its application to non-circular trajectories. Furthermore, the ability to improve image quality using non-circular orbits in conjunction with this calibration method was demonstrated. Conclusion: The proposed method has been shown feasible for conventional circular CBCT scans and offers a promising tool for non-circular scan orbits that can improve image quality, reduce dose, and extend field of view.