You can use the getc() function on a filehandle:

open FILE, "file" or die "can't read file: $!";
$char = getc FILE;
close FILE;
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You can set $/ to a reference to 1:

open FILE, "file" or die "...: $!";
{
  local $/ = \1;
  $char = <FILE>;
}
close FILE;
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Or use read() or sysread():

open FILE, "file" or die "yeah, $!";
read FILE, $char, 1;
# or sysread FILE, $char, 1;
close FILE;
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Any additional error checking is an exercise to the reader.