We present a joint experimental and theoretical study that demonstrates how to efficiently control a canted state of magnetization in Fe films grown on Ag(001) vicinal surface and precisely characterize it with the magneto-optical Kerr effect. It is shown that by employing different mechanisms to tune the magnetization tilting angle, any magnetization orientation within the plane perpendicular to the step edges can be achieved. In particular, increasing the Fe film thickness leads to continuous rotation of the magnetization easy axis toward the film surface and the sense of this rotation in uncovered films is opposite to that in films covered with Au. Another tuning mechanism is provided by oscillatory changes of the tilting angle at low temperatures due to formation of quantum well states in Fe films. The observed canting of magnetization is explained within a phenomenological model by an interplay of the shape anisotropy and two magnetocrystalline anisotropy terms, perpendicular and step-induced anisotropies, which results in an effective uniaxial magnetic anisotropy. The fitted thickness dependencies of the anisotropy constants accurately reproduce experimental variations of the tilting angle with both Fe and Au thicknesses as well as transient changes of the magnetization orientation in ultrathin Fe films upon submonolayer Au coverage, observed with spin-polarized low-energy electron microscopy.