A simple model is developed to describe the adsorption and the surface ordering in solutions of rigid-rodlike molecules. We focus here on the planar adsorption of the rigid rods restricting the orientations to two mutually orthogonal directions which are both parallel to the surface. When the bulk concentration increases, the adsorbed amount is increased and the adsorption isotherm has a kink at a bulk concentration phi(c), where the second-order isotropic-nematic transition (INT) takes place in a surface. Further increasing concentration, the adsorbed amount jumps at a bulk critical concentration phi(IN), where the first-order INT takes place in the bulk phase. For various values of the axial ratio of the rigid rods, the solvent conditions, and the adsorption energy, we examine the adsorption isotherms, the surface tensions, and the surface ordering. We also discuss the co-occurrences between the adsorption phenomena and the phase separation of a surface phase.