A method for generating random signals with characteristics resembling actual nuclear signals, suitable for testing ex-core nuclear measurement systems, is proposed and implemented through an algorithm. The time intervals between pulses of actual nuclear signal outputs follow an exponential distribution pattern. By calculating random numbers that adhere to the exponential distribution, it is possible to simulate the arrival time of each pulse, subsequently obtaining the count rate and output waveform. The developed random signal is generated by a computer-controlled signal generator, employing two control schemes: real-time updating of the signal generator frequency and controlling the signal generator to output arbitrary waveforms. The output count rate of the random signal can range from 1 to 106 cps. Finally, the random signals are validated using a scaler and an ex-core nuclear measurement system. The results indicate that the counts of the random signals measured by the scaler follow a theoretical Poisson distribution over a period of time. Additionally, during the assumed startup phase of the nuclear reactor, the fluctuating curves of count rates and reactor periods over time obtained by the ex-core nuclear measurement system exhibit similar randomness to actual nuclear signals, confirming the correctness and validity of this method.