SELECT i.index_name,c.column_name
FROM user_ind_columns c, user_indexes i
where c.index_name=i.index_name and c.table_name=i.table_name
and i.TABLE_NAME='my_table_name'
and i.TABLE_OWNER='my_schema_name'
See also:
How to get index column names of a table from DB2
How to get index column names of a table from SQL Server
How to get index column names of a table from MySQL
How to get index column names of a table from PostgreSQL
How to get index column names of a table from SQLite
Some Oracle tools you can try: https://www.withdata.com/oracle/