Let a sequence \Lambda \subset {\mathbb {C}} be such that the corresponding system of exponential functions {\mathcal {E}}(\Lambda ):=\left\{ {\text {e}}^{i\lambda t}\right\} _{\lambda \in \Lambda } is complete and minimal in L^2(-\pi ,\pi ), and thus each function f\in L^2(-\pi ,\pi ) corresponds to a nonharmonic Fourier series in {\mathcal {E}}(\Lambda ). We prove that if the generating function G of \Lambda satisfies the Muckenhoupt (A_2) condition on {\mathbb {R}}, then this series admits a linear summation method. Recent results show that the (A_2) condition cannot be omitted.