Quantum-well (QW) devices have been extensively investigated in semiconductor structures. More recently, spin-polarized QWs were integrated into magnetic tunnel junctions (MTJs). In this Letter, we demonstrate the spin-based control of the quantized states in iron 3d-band QWs, as observed in experiments and theoretical calculations. We find that the magnetization rotation in the Fe QWs significantly shifts the QW quantization levels, which modulate the resonant-tunneling current in MTJs, resulting in a tunneling anisotropic magnetoresistance (TAMR) effect of QWs. This QW-TAMR effect is sizable compared with other types of TAMR effect, and it is present above room temperature. In a QW MTJ of Cr/Fe/MgAl2O4/top electrode, where the QW is formed by a mismatch between Cr and Fe in the d band with Δ1 symmetry, a QW-TAMR ratio of up to 5.4% was observed at 5 K, which persisted to 1.2% even at 380 K. The magnetic control of QW transport can open new applications for spin-coupled optoelectronic devices, ultrathin sensors, and memory.