The stability of thermoacoustic systems is often regulated by the time delay between acoustic perturbations and corresponding heat release fluctuations. An accurate estimate of this value is of great importance in applications since even small modifications can introduce significant changes in the system behavior. Different studies show that the nonlinear delayed dynamics typical of these systems can be well captured with low-order models. In this work, a method is introduced to estimate the most likely value of the time delay of a single thermoacoustic mode from a measured acoustic pressure signal. The mode of interest is modeled by an oscillator equation, with a nonlinear delayed forcing term modeling the deterministic flame contribution and an additive white Gaussian noise to embed the stochastic combustion noise. Additionally, other thermoacoustic relevant parameters are estimated. The model accounts for a flame gain, for a flame saturation coefficient, for linear acoustic damping, and for the background combustion noise intensity. The pressure data time series is statistically analyzed and the set of unknown parameters is identified. Validation is performed with respect to synthetically generated time series and low order model simulations, for which the underlying delay is known a priori. A discussion follows about the accuracy of the method, in particular, a comparison with existing methods is drawn.