@text_lines = <STDIN>;
chomp($text_lines);
[download]

The statement  chomp($text_lines); chomp-s the (nonexistent) scalar  $text_lines not the  @text_lines array. Always

use warnings;
use strict;
[download]

at the start of your scripts. (Update: Actually, it's not accurate to describe  $text_lines as "nonexistent": if strictures are not enabled (see strict), just referring to such a variable causes Perl to call it into existence. This is known as autovivification (see perlglossary), and such a scalar is initialized with a default value of undef. However, chomp-ing undef doesn't do very much, and the script never accesses  $text_lines anywhere else, so...)

$column = <STDIN>;
[download]

This leaves  $column un-chomp-ed.

say "$ruler" x $column;
[download]

Not sure what this is supposed to do.

rrrrr eeeeee tyyyyy
[download]

This is just one line.

c:\@Work\Perl\monks>perl -le
"use 5.010;
 ;;
 use warnings;
 use strict;
 ;;
 say 'Please enter a few lines of text. Press ctrl-Z when finished';
 my @text_lines = <STDIN>;
 chomp(@text_lines);
 ;;
 say 'Please enter the width of the column: ';
 my $column = <STDIN>;
 chomp $column;
 ;;
 my $ruler = '1234567890';
 say $ruler x $column;
 ;;
 foreach (@text_lines) {
   printf qq{%${column}s\n}, $_;
   }
"
Please enter a few lines of text. Press ctrl-Z when finished
xyzzy
now is the time for all good men
x
foo bar
^Z
Please enter the width of the column:
7
1234567890123456789012345678901234567890123456789012345678901234567890
  xyzzy
now is the time for all good men
      x
foo bar
[download]

(Run under Windoze, so had to use ^Z instead of ^D.)

Update: Try
    printf qq{%*s\n}, $column, $_;
as an experiment (see * format specifier in sprintf specifier definitions).
(Update: Tried that? Ok, now try
    printf qq{%*.*s\n}, $column, $column, $_;
also.)