Loop-current (LC) order and the associated time-reversal symmetry breaking (TRSB) are pivotal for understanding hidden magnetism and unconventional superconductivity in strongly correlated quantum materials. The recently discovered kagome metal CsV₃Sb₅ provides a unique platform for exploring these intertwined phenomena. In this study, we utilize ¹²¹Sb nuclear quadrupole resonance (NQR) and ⁵¹V nuclear magnetic resonance (NMR) measurements to investigate the possible existence of the LC order in CsV₃Sb₅. Below T^∗ ≈ 45 K, we observe a field-independent NMR linewidth broadening at the V site in a high-quality single crystal, which indicates an internal magnetic field of 3.6 Oe at the V position. We show that this internal field arises from a static LC state that produces orbital magnetic moments μ_(rm orb) ranging from 0.002 to 0.01 μ_B. Detailed analysis suggests that the observed LC state breaks C₆ rotational symmetry to possess a low symmetry of C₂. Our results provide microscopic evidence for LC order in the charge density wave (CDW) phase of CsV₃Sb₅ and show that TRSB is intertwined with electronic nematicity, imposing stringent constraints on microscopic descriptions of the kagome CDW and its relation to superconductivity.