You need to use double quotes to have variables getting expanded:
Variable parsing
When a string is specified in double quotes or with heredoc, variables are parsed within it.
So:
"http://search.twitter.com/search.atom?lang=en&q=$q&rpp=100&page=1"
But it would be even better if you use proper URL escaping with urlencode:
'http://search.twitter.com/search.atom?lang=en&q='.urlencode($q).'&rpp=100&page=1'
You can also do that when declaring the $q variable and then use the double quoted string delcaration:
$q = urlencode($_GET['q']);
$rss = simplexml_load_file("http://search.twitter.com/search.atom?lang=en&q=$q&rpp=100&page=1");