To politicize something is to make it into a political issue. Candidates often politicize school performance, blaming low test scores on the policies of their opponents.
When you politicize an issue, you bring it into the realm of politics, whether it belongs there or not. Politicians may rush to politicize an oil spill, for example, using it as an example of why the country should switch to alternative energy sources. A candidate running for mayor will be quick to politicize a private scandal by the current mayor, making it an issue in the campaign. The Greek root is politikos, "of citizens, or pertaining to the state."