We present a new code for fitting radial velocities of stellar binaries and exoplanets using an Adaptive Simulated Annealing (ASA) global minimisation method. ASA belongs to the family of Monte Carlo methods and its main advantages are that it only needs evaluations of the objective function, it does not rely on derivatives, and the parameters space can be periodically redefined and rescaled for individual parameters. ASA is easily scalable since the physics is concentrated in only one function and can be modified to account for more complex models. Our ASA code minimises the χ^2 function in the multidimensional parameters space to obtain the full set of parameters (P, T_p, e, ω, γ, K_1, K_2) of the keplerian radial velocity curves which best represent the observations. As a comparison we checked our results with the published solutions for several binary stars and exoplanets with available radial velocities data. We achieve good agreement within the limits imposed by the uncertainties.