The availability of astrometric data and radial velocities of carbon stars near the Galactic plane enables us to investigate the kinematics of the Milky Way, especially the rotation curve. The recently published Third U.S. Naval Observatory CCD Astrograph Catalog (UCAC3) provides the opportunity to test this problem using three-dimensional velocity in order to obtain more reliable rotation curves. We intend to study the Galactic rotation curve up to 15kpc using the radial velocities and proper motions of carbon stars. The motivation for using UCAC3 is to provide high precision proper motions which have hardly been used in determining the rotation velocity of tracers. Seventy-four carbon stars and carbon-rich Mira variables toward the anti-center direction (90{deg}<l<270{deg}, |b|<6{deg}) are picked up from the literature then matched with UCAC3 carbon star candidates to obtain their proper motions. A rigorous geometrical method is employed to compute the rotation velocity of each object. Taking carbon stars as tracers, we find a flat rotation curve of 210+/-12km/s assuming R0=8.0kpc for the galactocentric distance and V0=220km/s for the rotation velocity of the Sun. Due to the uncertainties of distances, the rotation velocities are more dispersed if tangential velocities enter the calculation, compared to those derived from radial velocities only. However, the whole rotation curve shows coherence with previous results. Increasing observation and study of carbon stars would be desirable in order to provide more homogeneous data for the kinematical study of the Galactic disk.