SQL> get test_file
  1  create or replace procedure test_file
  2  as
  3    l_file          utl_file.file_type;
  4    l_buffer        varchar2(2000);
  5    l_textbit       varchar2(2000);
  6    l_old_delimiter number;
  7    l_new_delimiter number;
  8    l_eol           boolean;
  9  begin
 10    l_old_delimiter := 1;
 11    l_new_delimiter := 0;
 12    l_file := utl_file.fopen('z:MyWork', 'test.txt', 'r');
 13    begin
 14      --
 15      -- Loop through all lines in file
 16      --
 17      loop
 18        --
 19        -- Reset positions
 20        --
 21        l_old_delimiter := 1;
 22        l_new_delimiter := 0;
 23        --
 24        -- Read next line
 25        --
 26        utl_file.get_line(l_file, l_buffer);
 27        --
 28        -- For clarity, print out complete line
 29        --
 30        dbms_output.put_line(l_buffer);
 31        l_eol := false;
 32        while not l_eol
 33        loop
 34          --
 35          -- Determine position of next delimiter
 36          --
 37          l_new_delimiter := instr(l_buffer, ',', l_old_delimiter);
 38          if l_new_delimiter = 0
 39          then
 40            --
 41            -- Stop loop; no more delimiters found
 42            --
 43            l_eol := true;
 44            --
 45            -- Last field must still be displayed
 46            --
 47            l_textbit := substr(l_buffer, l_old_delimiter);
 48            dbms_output.put_line(l_textbit);
 49          else
 50            --
 51            -- Field is text starting at old_delimiter with length (new - old delimiter)
 52            --
 53            l_textbit := substr(l_buffer, l_old_delimiter, instr(l_buffer, ',', l_new_delimiter) - l_old_delimiter);
 54            dbms_output.put_line(l_textbit);
 55            l_old_delimiter := l_new_delimiter + 1;
 56          end if;
 57        end loop;
 58      end loop;
 59    exception
 60      when no_data_found
 61      then
 62        --
 63        -- Close file
 64        --
 65        utl_file.fclose(l_file);
 66    end;
 67* end;
SQL> /

Procedure created.

SQL> set serveroutput on size 1000000
SQL> exec test_file
This,is,my,first,line
This
is
my
first
line
And,this,is,my,second,line
And
this
is
my
second
line

PL/SQL procedure successfully completed.