Let's have a look at what IUPAC say; they would be a reliable source to get definitions of chemical terminology from:
"A substance composed of monomer molecules."
"A molecule which can undergo polymerization thereby contributing
constitutional units to the essential structure of a macromolecule. "
"A substance composed of macromolecules."
"A molecule of high relative molecular mass, the structure of which
essentially comprises the multiple repetition of units derived,
actually or conceptually, from molecules of low relative molecular
These definitions are consistent with the latest IUPAC Compendium of Polymer Terminology and Nomenclature, IUPAC Recommendations 2008
Note that, historically, the definition of a polymer has changed somewhat. Up until about 80 years ago, polymers were seen as molecules comprised of similar empirical formula - benzene, for example, was considered a polymer of acetylene. It was Staudinger's work in the 1920's (contributing to his Nobel Prize) that defined polymers as macromolecules.