Order matters in a regular expression, so I think your only option is to use a loop to check for all of the characters (update: this is essentially the same as your code):

sub has_all {
  my $text = shift;
  for my $c ('a', 'r', 'z', 'x') {
    return 0 unless $text =~ m/$c/;
  }
  1;
}
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Update: Well, I guess I was wrong, and it can be done in a single regex. Now I'm going to have to start thinking about how else I can use lookaheads.