The excitations in the Kitaev spin liquid (KSL) can be described by Majorana fermions, which have characteristic field dependence of bulk gap and topological edge modes. In the high-field state of layered honeycomb magnet $\alpha \text{-}{\mathrm{RuCl}}_3$, experimental results supporting these Majorana features have been reported recently. However, there are challenges due to sample dependence, and the impact of inevitable disorder on the KSL is poorly understood. Here, we study how low-energy excitations are modified by introducing point defects in $\alpha \text{-}{\mathrm{RuCl}}_3$ using electron irradiation, which induces site vacancies and exchange randomness. High-resolution measurements of the temperature dependence of specific heat $C(T)$ under in-plane fields $H$ reveal that, while the field-dependent Majorana gap is almost intact, additional low-energy states with $C/T=A(H)T$ are induced by introduced defects. At low temperatures, we obtain the data collapse of $C/T\sim H^{-\gamma }(T/H)$ expected for a disordered quantum spin system but with an anomalously large exponent $\gamma$. This leads us to find a power-law relationship between the coefficient $A(H)$ and the field-sensitive Majorana gap. These results are consistent with the picture that the disorder induces low-energy linear Majorana excitations, which may be considered as a weak localization effect of Majorana fermions in the KSL.