Using counterpropagating surface plasmon polaritons (SPPs) on a gold stripe, we demonstrate a scannable integrated optical tweezer. We demonstrate the trapping of individual fluorescent beads on the stripe, which supports a single quasi-transverse magnetic (TM) mode at the metal-water interface. The beads are localized to the stripe center, with a standard deviation of 51 nm transverse to the stripe, corresponding to a trap stiffness of 1.7 pN/microm. The localization along the stripe is achieved by balancing the scattering forces from the two counterpropagating SPPs excited by prism coupling. The particle position along the stripe can be controlled by varying the relative intensity of the two input beams. This work adds an important new capability to plasmonic optical tweezers, that of scanning. We anticipate that this will broaden the range of applications of plasmonic optical manipulation.