If you can slurp the file, you can reduce the time by 75%. See the comments after the end block show various steps to arriving at this:

#! perl -sw
use 5.010;
use strict;
use Time::HiRes qw[ time ];

my $start = time;

my $size = -s $ARGV[ 0 ];
die("File not a multiple of 4 bytes")
    unless ( $size % 4 ) == 0;

open my $fh, "<:raw", $ARGV[ 0 ]  or die;
my $data;
{
    local $/;
    $data = <$fh>;
}
close $fh;
open $fh, '<', \$data;

my $check_value = 0;
my $buf;

while( read( $fh, $buf, 4 ) ) {

    $check_value ^= unpack 'L', $buf;
    $check_value = ( ( $check_value & 0x7fffffff ) << 1 )
        | ( $check_value >> 31 );
}

say $check_value;

printf "Took: %f seconds\n", time() -$start;

__END__
## Original code
C:\test>767001.pl 767001-small.dat
2779316821
Took: 13.011000 seconds

## Eliminate in loop conditions;
C:\test>767001.pl 767001-small.dat
2779316821
Took: 11.577000 seconds

## Use Ikegami's re-write
C:\test>767001.pl 767001-small.dat
2779316821
Took: 10.453000 seconds

## Use RAM-file
C:\test>767001.pl 767001-small.dat
2779316821
Took: 3.148000 seconds
[download]

However, then I tried a different tack--reading and processing the file in larger chunks--and halved that again while eliminating the slurp limitation. Again see the comments, but 64K chunks seems optimal on my system:

#! perl -sw
use 5.010;
use strict;
use Time::HiRes qw[ time ];
use constant BUFSIZ => 64 * 1024;

my $start = time;

my $size = -s $ARGV[ 0 ];
die("File not a multiple of 4 bytes")
    unless ( $size % 4 ) == 0;

open my $fh, "<:raw", $ARGV[ 0 ]  or die;

my $check_value = 0;
my $buf;

while( read( $fh, $buf, BUFSIZ ) ) {

    for ( unpack 'L*', $buf ) {
        $check_value ^= $_;
        $check_value = ( ( $check_value & 0x7fffffff ) << 1 )
            | ( $check_value >> 31 );
    }
}

say $check_value;

printf "Took: %f seconds\n", time() -$start;

__END__
## Process 4K chunks
C:\test>767001-buk 767001-small.dat
2779316821
Took: 1.771000 seconds

## Process 16K chunks
C:\test>767001-buk 767001-small.dat
2779316821
Took: 1.750000 seconds

## Process 64K chunks
C:\test>767001-buk 767001-small.dat
2779316821
Took: 1.775000 seconds

...
## Process 256K chunks
C:\test>767001-buk 767001-small.dat
2779316821
Took: 1.804000 seconds
[download]

But for ultimate speed, combine the above technique with some Inline::C and you can reduce the time to 1/1000th of your original:

#! perl -sw
use 5.010;
use strict;
use Inline C => Config => BUILD_NOISY => 1;
use Inline C => <<'END_C',  NAME => '_767001', CLEAN_AFTER_BUILD => 0;

U32 checksum( U32 sum, SV *buf ) {
    int i;
    int n = SvCUR( buf ) >> 2;
    U32 *p = (U32 *)SvPVX( buf );

    for( i = 0; i < n; ++i ) {
            sum ^= p[ i ];
        sum = ( ( sum & 0x7fffffff ) << 1 ) | ( sum >> 31 );
    }
    return sum;
}

END_C

use Time::HiRes qw[ time ];
use constant BUFSIZ => 64 * 1024;

my $start = time;

my $size = -s $ARGV[ 0 ];
die("File not a multiple of 4 bytes")
    unless ( $size % 4 ) == 0;

open my $fh, "<:raw", $ARGV[ 0 ]  or die;

my $sum = 0;
my $buf;

while( read( $fh, $buf, BUFSIZ ) ) {
    $sum = checksum( $sum, $buf );
}

say $sum;

printf "Took: %f seconds\n", time() -$start;

__END__
C:\test>767001-IC 767001-small.dat
2779316821
Took: 0.014622 seconds
[download]