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 tweet's content alone. I propose a method of ranking tweets by generating a reputation score for each tweet that is based not just on content, but also additional information from the Twitter ecosystem that consists of users, tweets, and the web pages that tweets link to. This information is obtained by modeling the Twitter ecosystem as a three-layer graph. The reputation score is used to power two novel methods of ranking tweets by propagating the reputation over an agreement graph based on tweets' content similarity. Additionally, I show how the agreement graph helps counter tweet spam. An evaluation of my method on 16~million tweets from the TREC 2011 Microblog Dataset shows that it doubles the precision over baseline Twitter Search and achieves higher precision than current state of the art method. I present a detailed internal empirical evaluation of RAProp in comparison to several alternative approaches proposed by me, as well as external evaluation in comparison to the current state of the art method.