That's an anagram problem, which has a canonical answer. First absorb your dictionary in a hash:

my %words;
{
    open my $fh, '<', '/path/to/dict.txt' or die $!;
    while <$fh> {
        chomp;
        my $key = join '', sort split '';
        push @{$words{$key}}, $_;
    }
}
[download]

That collects your data, now just rearrange your input word to make a key and print the associated words:

my $word = <>; # or however you get it
chomp;
$word = join '', sort split '', $word;
print "@{$words{$word}}\n";
[download]

Alphabetizing and mushing together the characters of a word provides a key for anagrams..

If this is used a lot or the dictionary is big, you may want to keep the "hash" in a database.