The increasing popularity of Twitter renders improved trustworthiness and relevance assessment of tweets much more important for search. However, given the limitations on the size of tweets, it is hard to extract measures for ranking from the tweets' content alone. We present a novel ranking method called RAProp, which combines two orthogonal measures of relevance and trustworthiness of a tweet. The first, called Feature Score, measures the trustworthiness of the source of the tweet by extracting features from a 3-layer Twitter ecosystem consisting of users, tweets and webpages. The second measure, called agreement analysis, estimates the trustworthiness of the content of a tweet by analyzing whether the content is independently corroborated by other tweets. We view the candidate result set of tweets as the vertices of a graph, with the edges measuring the estimated agreement between each pair of tweets. The feature score is propagated over this agreement graph to compute the top-κ tweets that have both trustworthy sources and independent corroboration. The evaluation of our method on 16 million tweets from the TREC 2011 Microblog Dataset shows that for top-30 precision, we achieve 53% better precision than the current best performing method on the data set, and an improvement of 300% over current Twitter Search.