Because you admitted unabashedly you're new to Perl, and because you pleaded very graciously for our help, I've taken the liberty of refactoring your script a tiny bit. I've incorporated idioms of Modern Perl and a few Perl best practices gleaned from Perl Best Practices.

#!perl
#
# hiragana2romaji.pl - Convert hiragana text to romaji text

use strict;
use warnings;
use autodie;

use Lingua::JA::Moji qw( kana2romaji );

@ARGV == 2
    or die "Usage: perl $0 <hiragana file> <romaji file>\n";

my $hiragana_file = shift @ARGV;
my $romaji_file   = shift @ARGV;

open my $hiragana_fh, '<:encoding(UTF-8)', $hiragana_file;
open my $romaji_fh,   '>:encoding(UTF-8)', $romaji_file;

while (my $hiragana_text = <$hiragana_fh>) {
    chomp $hiragana_text;
    my $romaji_text = kana2romaji($hiragana_text);
    print {$romaji_fh} "$romaji_text\n";
}

close $hiragana_fh;
close $romaji_fh;

exit 0;
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