RADIO observations using very-long-baseline interferometry (VLBI) can measure the deflection of electromagnetic radiation by the Sun's gravitational field with an accuracy of better than 1 milliarcsecond, and can thus be used to test General Relativity. For an object at an angle-alpha from the centre of the Sun, the expected deflection is 1 (1 + gamma) (M(s)/r(e))((1 + cos-alpha)/(1 - cos-alpha)) 1/2, where M(s) is the mass of the Sun in geometrized units 2 (1.477 x 10(5) cm), r(e) is the distance from the Earth to the Sun in cm, and gamma is a parameter whose value is 1 if General Relativity is correct but which takes on different values in other theories of gravity. For gamma = 1, the deflection is 1,750 mas at the Sun's limb, 4 mas at alpha = 90-degrees and 0 at alpha = 180-degrees. Our analysis of ten years of VLBI data, including observations of objects in the range 2.5-degrees < alpha < 178-degrees, yields an estimate gamma = 1.0002 with a formal standard error of 0.00096 and an estimated standard error of 0.002. This determination is comparable in accuracy and in good agreement with the determination from Mars-Viking time-delay measurements 3.