PL SQL Data Types Oracle PLSQL Tutorial

You cannot store time zone into DATE datatype.
You can explicitly store the time zone for TIMESTAMP datatypes, as shown here:

declare
    variable1_ts TIMESTAMP[(precision)] WITH TIME ZONE;
begin
    NULL;
end;
/

SQL>
SQL> --You can see these values yourself by using the built-in functions DBTIMEZONE and SESSIONTIMEZONE.
SQL>
SQL> declare
  2      v_ts TIMESTAMP(6) WITH TIME ZONE :=CURRENT_TIMESTAMP;
  3      v_tx VARCHAR2(2000);
  4  begin
  5      v_tx:=to_char(v_ts,'HH24:MI:SS.FF6 TZR');
  6      DBMS_OUTPUT.put_line(v_tx);
  7      v_tx:=to_char(v_ts,'TZH TZM');
  8      DBMS_OUTPUT.put_line(v_tx);
  9  end;
 10  /
20:32:41.890000 -07:00
-07 00
PL/SQL procedure successfully completed.
SQL>