I found this forum: http://www.orafaq.com/forum/t/60583/0/. It may be what you are looking.
Basically, you can use the Oracle supplied dbms_utility.format_call_stack:
scott@ORA92> CREATE TABLE error_tab
  2    (who_am_i      VARCHAR2(61),
  3     who_called_me VARCHAR2(61),
  4     call_stack    CLOB)
  5  /
Table created.
scott@ORA92> 
scott@ORA92> CREATE OR REPLACE PROCEDURE d
  2  AS
  3    v_num      NUMBER;
  4    v_owner    VARCHAR2(30);
  5    v_name     VARCHAR2(30);
  6    v_line     NUMBER;
  7    v_caller_t VARCHAR2(100);
  8  BEGIN
  9    select to_number('a') into v_num from dual; -- cause error for testing
 10  EXCEPTION
 11    WHEN OTHERS THEN
 12      who_called_me (v_owner, v_name, v_line, v_caller_t);
 13      INSERT INTO error_tab
 14      VALUES (who_am_i,
 15          v_owner || '.' || v_name,
 16          dbms_utility.format_call_stack);
 17  END d;
 18  /
Procedure created.
scott@ORA92> SHOW ERRORS
No errors.
scott@ORA92> CREATE OR REPLACE PROCEDURE c
  2  AS
  3  BEGIN
  4    d;
  5  END c;
  6  /
Procedure created.
scott@ORA92> CREATE OR REPLACE PROCEDURE b
  2  AS
  3  BEGIN
  4    c;
  5  END b;
  6  /
Procedure created.
scott@ORA92> CREATE OR REPLACE PROCEDURE a
  2  AS
  3  BEGIN
  4    b;
  5  END a;
  6  /
Procedure created.
scott@ORA92> execute a
PL/SQL procedure successfully completed.
scott@ORA92> COLUMN who_am_i FORMAT A13
scott@ORA92> COLUMN who_called_me FORMAT A13
scott@ORA92> COLUMN call_stack    FORMAT A45
scott@ORA92> SELECT * FROM error_tab
  2  /
WHO_AM_I      WHO_CALLED_ME CALL_STACK
------------- ------------- ---------------------------------------------
SCOTT.D       SCOTT.C       ----- PL/SQL Call Stack -----
                              object      line  object
                              handle    number  name
                            6623F488         1  anonymous block
                            66292138        13  procedure SCOTT.D
                            66299430         4  procedure SCOTT.C
                            6623D2F8         4  procedure SCOTT.B
                            6624F994         4  procedure SCOTT.A
                            66299984         1  anonymous block
scott@ORA92>