Kagome metals with van Hove singularities near the Fermi level can host intriguing quantum phenomena such as chiral loop currents, electronic nematicity, and unconventional superconductivity. However, to our best knowledge, unconventional magnetic states driven by van Hove singularities–like spin-density waves–have not been observed experimentally in kagome metals. Here, we report the magnetic and electronic structure of the layered kagome metal CeTi₃Bi₄, where Ti kagome electronic structure interacts with a magnetic sublattice of Ce³⁺J_eff = 1/2 moments. Neutron diffraction reveals an incommensurate spin-density wave ground state of the Ce³⁺ moments, coexisting with commensurate antiferromagnetic order across most of the temperature-field phase diagram. The commensurate component is preferentially suppressed by thermal fluctuations and magnetic field, yielding a rich phase diagram involving an intermediate single-Q spin-density wave phase. First-principles calculations and angle-resolved photoemission spectroscopy identify van Hove singularities near the Fermi level, with the observed magnetic propagation vectors connecting their high density of states, strongly suggesting a van Hove singularity-assisted spin-density wave. These findings establish kagome metals LnTi₃Bi₄ as a model platform where the characteristic electronic structure of the kagome lattice plays a pivotal role in magnetic order.