We demonstrate an integrated optical probe including an on-chip microlens for a common-path swept-source optical coherence tomography system. This common-path design uses the end facet of the silicon oxynitride waveguide as the reference plane, thus eliminating the need of a space-consuming and dispersive on-chip loop reference arm, thereby obviating the need for dispersion compensation. The on-chip micro-ball lens eliminates the need of external optical elements for coupling the light between the chip and the sample. The use of this lens leads to a signal enhancement up to 37 dB compared to the chip without a lens. The light source, the common-path arm and the detector are connected by a symmetric Y junction having a wavelength independent splitting ratio (50/50) over a much larger bandwidth than can be obtained with a directional coupler. The signal-to-noise ratio of the system was measured to be 71 dB with 2.6 mW of power on a mirror sample at a distance of 0.3 mm from the waveguide end facet. Cross-sectional OCT images of a layered optical phantom sample are demonstrated with our system. A method, based on an extended Fourier-domain OCT model, for suppressing ghost images caused by additional parasitic reference planes is experimentally demonstrated.