Gold nanorods (GNRs) are of special interest in nanotechnology and biomedical applications due to their biocompatibility, anisotropic shape, enhanced surface area, and tunable optical properties. The use of GNRs, for example, as sensors and mechanical actuators, relies on the ability to remotely control their orientation as well as their translational and rotational motion, whether individually or in groups. Achieving such particle control by using optical tools is challenging and exceeds the capabilities of conventional laser tweezers. We present a tool that addresses this complex manipulation problem by using a curve-shaped laser trap, enabling the optical capture and programmable transport of single and multiple GNRs along any trajectory. This type of laser trap combines confinement and propulsion optical forces with optical torque to transport the GNRs while simultaneously controlling their rotation (spinning) and orientation. The proposed system facilitates the light-driven control of GNRs and the quantitative characterization of their motion dynamics including transport speed, spinning frequency, orientation, and confinement strength. We experimentally demonstrate that remote control of the GNRs can be achieved both near a substrate surface (2D trapping) and deep within the sample (3D all-optical trapping). The motion dynamics of two sets of off-resonant GNRs, possessing similar aspect ratios but different resonance wavelengths, are analyzed to highlight the role played by their optical and mechanical properties in the optical manipulation process. The experimental results are supported by a theoretical model describing the observed motion dynamics of the GNRs. This optical manipulation tool can significantly facilitate applications of light-driven nanorods.