Here's another option:

use strict;
use warnings;

while(<>){
    print ">Leaf_$.\n$_";
}

Usage: perl script.pl inFile [>outFile]

The last, optional parameter directs output to a file.

As a oneliner: perl -ne 'print ">Leaf_$.\n$_"' inFile [>outFile]

Output on your dataset:

>Leaf_1
AGCCCTCTGTAGCATTTGTATGGC
>Leaf_2
AGCCCTCTGTAGTATTTCTATGGC
>Leaf_3
AGCCCTCTGTAGTATTTGTATGGCTCCTTAGAC

Both take advantage of Perl's $. variable which contains the line number of the file being read.

Hope this helps!

Proper programming practice is to use strict and warnings.

And you need to chomp the file to remove new line characters. Try this code for e.g.,

use strict;
use warnings;

if (@ARGV != 1) {
    die "Usage: print_fasta.pl <raw_input_file>\n";
}

open(IN, $ARGV[0]) or die "Error!! Cannot open $ARGV[0]: $!\n";
open(OUT, ">Output.fa") or die "Error!! Cannot create the file: $!\n";

my @file = <IN>;
chomp(@file);
my $count = 1;

foreach my $line (@file) {
    print OUT ">Leaf_$count\n";
    print OUT "$line\n";
    $count++;
}

NOTE: Here I'm assuming that all the lines in the text file only have the sequence in each line, like in your example.

Warning: I am also not a professional, but the following works :)

$ perl below-script.pl input-sequences.txt

#!/usr/bin/perl                                                             

open (INPUT, $ARGV[0]) or die $!;                                           
open (OUTPUT, ">Output.fa");                                                

my $count = 1;                                                              
while (<INPUT>){                                                            
    chomp;                                                                  
    print OUTPUT ">Leaf_$count\n$_\n";                                      
    $count += 1;                                                            
}                                                                           

close (OUTPUT);                                                             
close (INPUT);