A method for measuring mooring line tension is proposed based on observation of the natural frequencies of the mooring line segment between the winch and the fairlead. The anchor line tension is observed through the string equation where an analytical expression for the line's eigen-frequencies is obtained. The tension is observed on line by utilizing a nonparametric system identification approach in which the peaks of a maximum entropy spectrum of the transverse acceleration measures of the vibrating string are automatically identified. The method is verified against full-scale data from the Troll B floating concrete oil production platform operating in the North Sea.