You do use chmod, but you have to keep in mind that unlike the command-line chmod, which can simply flip bits on or off, perl's chmod sets the entire permission set as a single unit. Basically, you have to read the current permissions off the file using stat, add group sticky to those permissions bitwise, and then apply the new permissions using chmod. I think the group sticky bit is 02000, so that'd be:

my $filename = 'filename';
my $perms    = ((stat($filename))[2] & 07777); # Just permissions, not
+ type
my $newperms = $perms ^ 02000;                 # Add the group sticky 
+bit
chmod $newperms, $filename or die "Could not change permissions: $!";
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