Testing alternative metric theories of gravity with an accuracy much better than the present level has recently drawn great attention, in particular in relation to the search for a very weak scalar field, a possible remnant of an early inflationary cosmology. The gravitational deflection of electromagnetic waves is controlled by the dimensionless post-Newtonian parameter , which takes a value of unity in general relativity. In this work we claim that the accuracy in the measurement of can be substantially improved by measuring the Doppler frequency shift of a microwave beam transponded back to the ground by an interplanetary spacecraft near solar conjunction. In this kind of experiment, the dispersion due to the plasma in the solar corona is the crucial difficulty, which, however, can be essentially overcome using skilful combinations of carriers with different frequencies. The spacecraft Cassini, launched in 1997, adopts a sophisticated radio system, including a Ka-band link at 32-34 GHz, which makes this possible. We discuss the noise budget for two experiments to be carried out with Cassini in 2002 and 2003. In particular, we consider the contribution of the solar corona, the non-gravitational accelerations, and thermal noise due to solar radio emission. We estimate that an accuracy in of about 10^-5 is achievable.