Technically, you could use the DBMS_METADATA package to get the DDL for the view in a CLOB and then parse that looking for a reference to your table. But there are far easier solutions than looking at the view definition.
Oracle maintains information about object dependencies in the USER_DEPENDENCIES view (or ALL_DEPENDENCIES or DBA_DEPENDENCIES depending on your privilege levels and whether you're trying to track dependencies across schemas). You're far better off using those views
SQL> create table base_table (
2 col1 number
3 );
Table created.
SQL> create view my_view
2 as
3 select *
4 from base_table;
View created.
SQL> select name, type
2 from user_dependencies
3 where referenced_name = 'BASE_TABLE';
NAME TYPE
------------------------------ ------------------
MY_VIEW VIEW
If you're using the USER_DEPENDENCIES view, you can also do more sophisticated things with the tree of dependent objects. If I create a second view that depends on the first, I can easily see that both views eventually use the base table.
SQL> create view my_view2
2 as
3 select *
4 from my_view;
View created.
SQL> ed
Wrote file afiedt.buf
1 select level, name, type
2 from user_dependencies
3 start with referenced_name = 'BASE_TABLE'
4* connect by referenced_name = prior name
SQL> /
LEVEL NAME TYPE
---------- ------------------------------ ------------------
1 MY_VIEW VIEW
2 MY_VIEW2 VIEW
