Detecting the spectroscopic signatures of relativistic quasiparticles in emergent topological materials is crucial for searching their potential applications. Magnetometry is a powerful tool for fathoming electrons in solids, by which a clear method for discerning relativistic quasiparticles has not yet been established. Adopting the probes of magnetic torque and parallel magnetization for the archetype Weyl semimetal TaAs in strong magnetic field, we observed a quasi-linear field dependent effective transverse magnetization and a non-saturating parallel magnetization when the system enters the quantum limit. Distinct from the saturating magnetic responses for non-relativistic quasiparticles, the non-saturating signals of TaAs in strong field is consistent with our newly developed magnetization calculation for a Weyl fermion system in an arbitrary angle. Our results establish a high-field thermodynamic method for detecting the magnetic response of relativistic quasiparticles in topological materials.