The 25-year-old joined the Railwaymen on a four-week deal last month, but he has now agreed to remain at Gresty Road until late November.
Speaking about his decision, Brandy told the club's official website: "From the moment I have come here everyone has made me feel welcome. The gaffer, the staff and the players have been great with me.
"Unfortunately when I first came here the results were not going away but we have turned the corner a bit in the last couple of games and hopefully me and the boys can continue to pick up some results and move up the table.
"At this stage of my career and the way things are panning out I want to be here. The gaffer has played in in the last couple of games and I think I've done reasonably well, so I just want to push on and show some more."
Brandy has scored one goal during his four appearances for the League One side.