There are plenty choirs in Singapore, but most of them aren't open to general public, e.g. university choir, church choir, etc. Other than those, you can try the Singapore Youth Choir http://www.syc.org.sg/
The Singapore Symphony Chorus (part of the Singapore Symphony Orchestra) http://www.symphonychorus.sg/
There's also the Amadeus Choral Society http://www.amadeus.org.sg/
If you're into opera you can try the Singapore Lyric Opera http://www.singaporeopera.com.sg/
Obviously you'll need to pass their auditions to be a singer in those groups. There are also a few other smaller community choirs. If you join any of the above you'll realise that many of them are also members of other choirs.