Argument search engines identify, extract, and rank the most important arguments for and against a given controversial topic. A number of such systems have recently been developed, usually focusing on classic information retrieval ranking methods that are based on frequency information. An important aspect that has been ignored so far by search engines is the quality of arguments. We present a quality-aware ranking framework for arguments already extracted from texts and represented as argument graphs, considering multiple established quality measures. An extensive evaluation with a standard benchmark collection demonstrates that taking quality into account significantly helps to improve retrieval quality for argument search. We also publish a dataset in which arguments with respect to topics were tediously annotated by humans with three widely accepted argument quality dimensions.