The syntax of join is,
join EXPR,list
I have just modified your code into the following.
use strict;
use warnings;
my @variable;
my $variable;
open(INFILE, "<perlfile.txt");
@variable=<INFILE>;
$variable =join(" ",@variable);
print "$variable";
close(INFILE);
open(OUTFILE, ">perlfile.txt");
$variable =~ s/0/zero/g ;
$variable =~ s/1/one/g ;
$variable =~ s/2/two/g ;
$variable =~ s/3/three/g ;
$variable =~ s/4/four/g ;
$variable =~ s/5/five/g ;
$variable =~ s/6/six/g ;
$variable =~ s/7/seven/g ;
$variable =~ s/8/eight/g ;
$variable =~ s/9/nine/g ;
print "$variable";
print OUTFILE "$variable","\n";
close(OUTFILE);