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The phenomena resulting from interaction between polymers and membranes pose important problems for biological applications. Based on a scaling theory, we investigate the spontaneous curvature of a membrane induced by either flexible or semiflexible chain adsorption. Irrespective of chain stiffness, a weakly adsorbed polymer induces the membrane to bend away (to have a positive curvature) from the polymer mostly due to increase of the conformational entropy compared with that for a flat surface. On the other hand, a strongly adsorbed polymer induces the membrane to bend toward the polymer mostly due to decrease in the interaction energy, leading to a possibility of encapsulation of polymer by the membrane.