We present a radial velocity survey of a sample of the field population of carbon stars in the outer parts of the Small Magellanic Cloud (SMC). This first set of results includes radial velocities for 71 carbon stars, with an individual precision of +/-2-5km/s. The mean heliocentric velocity of the stars (excluding one very high velocity star) is 149.3+/-3.0km/s with a velocity dispersion of 25.2+/-2.1km/s. These values drop to 145.5+/-2.7km/s and 20.6+/-1.9km/s respectively, if we exclude the stars belonging to the Outer Wing. The velocity distribution does not show the multiple peaks seen in some samples of Population I objects. The mass of the SMC as inferred from the above velocity dispersion (without the outer Wing stars) is =~1.2x10^9^M_{sun}_.