High-quality (001)-oriented (pseudo-cubic notation) ferromagnetic YTiO$_3$ thin films were epitaxially synthesized in a layer-by-layer way by pulsed laser deposition. Structural, magnetic and electronic properties were characterized by reflection-high-energy-electron-diffraction, X-ray diffraction, vibrating sample magnetometry, and element-resolved resonant soft X-ray absorption spectroscopy. To reveal ferromagnetism of the constituent titanium ions, X-ray magnetic circular dichroism spectroscopy was carried out using four detection modes probing complimentary spatial scale, which overcomes a challenge of probing ferromagnetic titanium with pure Ti3+(3d$^1$). Our work provides a pathway to distinguish between the roles of titanium and A-site magnetic rare-earth cations in determining the magnetism in rare-earth titanates thin films and heterostructures.