Použijte LIKE/regex s proměnnou v mongoidu

searchterm = (params[:searchlogparams][:searchterm])
@tweets = Tweet.any_of({ :text => Regexp.new ("/.*"+searchterm+".*/") })

nebo

searchterm = (params[:searchlogparams][:searchterm])
@tweets = Tweet.any_of({ :text => /.*#{searchterm}.*/ })