There is no exposed rejection counter.
The main purpose of DML Error Logging is to support ETL processes. It allows us to load huge amounts of data without a couple of errors forcing the entire load to rollback. I guess the underlying rationale is that errors will be resolved manually before we issue more DML against that table: it's not really intended to provide a permanent error log.
However, if you give each DML statement a unique tag you can count the exact number of rejections it has spawned.
declare
l_tag varchar2(46);
reject_cnt pls_integer;
begin
....
l_tag := 'merging from source_table::'||to_char(sysdate, 'yyyymmddhh24miss');
merge into target_table a
using source_table b
on (a.id = b.id)
....
log errors into err$_target_table (l_tag) reject limit 10;
select count(*)
into reject_cnt
from err$_target_table
where ora_err_tag$ = l_tag;
....