When a neuron receives a randomly fluctuating input current, its reliability of spike generation improves compared with the case of a constant input current [Mainen and Sejnowski, Science 268, 1503 (1995)]. This phenomenon can be interpreted as phase synchronization between uncoupled nonlinear oscillators subject to a common external input. We analyze this phenomenon using dynamical models of neurons, assuming the input current to be a simple random telegraphic signal that jumps between two values, and the neuron to be always purely self-oscillatory. The internal state of the neuron randomly jumps between two limit cycles corresponding to the input values, which can be described by random phase maps when the switching time of the input current is sufficiently long. Using such a random map description, we discuss the synchrony of neural oscillators subject to fluctuating inputs. Especially when the phase maps are monotonic, we can generally show that the Lyapunov exponent is negative, namely, phase synchronization is stable and reproducibility of spike timing improves.