In this Monte Carlo algorithm for polarizable force fields, the fluctuating charges are treated as special degrees of freedom subject to a secondary low-temperature thermostat in close analogy to the extended Lagrangian formalism commonly used in molecular dynamics simulations of such systems. The algorithm is applied to Berne's SPC-FQ (simple point charge-fluctuating charge) model for water. The robustness of the algorithm with respect to the temperature of the secondary thermostat and to the fraction of fluctuating-charge moves is investigated. With the new algorithm, the cost of Monte Carlo simulations using fluctuating-charge force fields increases by less than an order of magnitude compared to simulations using the parent fixed-charge force fields.