The easy (and a bit slower) way is to do a loop of update statements:

use strict;
use DBI;

my @left_column = do { open my $fh, "<", 'data/left_file.txt' };
my @right_column = do { open my $fh, "<", 'data/right_file.txt' };

chomp @left_column;
chomp @right_column;


my $dbh = DBI->connect(...);
my $sth = $dbh->prepare(<<SQL);
UPDATE wordtable SET right_column = ?
WHERE left_column = ?
SQL;

for my $index (0..$#left_column) {
    $sth->execute($right_column, $left_column);
};
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You will want to read about the placeholders in the DBI documentation.

A different approach might be to construct one huge CASE statement, but you might run against the query text size limits of your database:

my $statement = 'UPDATE wordtable SET right_column = CASE ';
$statement .= join "\n", map { "WHEN left_column = '$left_column[_]' T
+HEN '$right_column[$_]'" } 0..$#left_column;
$statement .= "END;";
print $statement;
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