A detailed zero-field and transverse-field muon spin relaxation/rotation (μSR) experiments have been carried out on the recently discovered noncentrosymmetric superconductor W₃Al₂C to speculate about its superconducting ground state. Bulk nature of superconductivity below 7.6 K is confirmed through magnetization and specific heat measurements. No change in the zero field μSR spectra collected above and below T_c is visible, ruling out the possibility of spontaneous magnetic field below T_c. This confirms that time-reversal symmetry is preserved for W₃Al₂C upon entering in the superconducting ground state. Temperature-dependent superfluid density [ρ_s(T)], which directly reflects the superconducting gap symmetry is obtained by the analysis of spectra obtained from the transverse-field μSR experiments. Despite a noncentrosymmetric structure, W₃Al₂C adopts a fully gapped spin-singlet superconducting ground state as confirmed through the analysis of ρ_s(T) and C_e(T). The zero-temperature value of gap is Δ₀ = 1.139(5) meV with gap-to-T_c ratio 2Δ₀/k_BT_c ≈ 3.48, classifying this material as a weakly coupled superconductors. We have also revealed that the ratio T_c/λ^-2_eff is comparable to the class of unconventional superconductors, which points towards an unconventional pairing mechanism in W₃Al₂C.