It would be easy if you just wanted to chop off the end of the file:

truncate('test.dat', 1024);
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But I assume since it's a log file that you want to chop off the beginning:

use strict;
use warnings;

my $fname = 'test.dat';
my $crop = 1024;

my $handle;
open($handle, $fname);
$_ = (stat($handle))[7];
if ($_ > $crop) {
    seek($handle, $_ - $crop, 0);
    read($handle, $_, $crop);
    close($handle);
    open($handle, ">$fname");
    print $handle $_;
}
close($handle);
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Of course, this method has problems too, in that additional lines could theoretically be appended to the file between the read and the write and therefore lost. File locking / unlocking probably isn't a viable solution, but you can just assume that up to x number of bytes might be written to the file between read and write, and edit your truncate accordingly:

my $crop = 1024;
my $margin = 64;
...
read($handle, $_, $crop + $margin);
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EDIT: zentara's solution solves that problem, and is much more elegant if you assume that the file will always be larger than the truncate size. ++