Can you really add cluster for an existing table? For instance...
I've got a table:

CREATE TABLE table_name(  
t_id number PRIMARY KEY,  
t_name varchar2(50));   


(c_id NUMBER) SIZE 100;

It is possible to command like: ALTER TABLE t_name ADD CLUSTER my_cluster(t_id); or something like that like this?
Because I would like table to appear something similar to this:

CREATE TABLE table_name(  
t_id number PRIMARY KEY,  
t_name varchar2(50))  
CLUSTER my_cluster(t_id); 

And shedding all connected tables is not really what I wish to do.

You may not know very well what a cluster is? From the docs:

"Groupings are categories of a number of tables physically saved together simply because they share common posts and therefore are frequently used together. Because related rows are physically saved together, disk access time enhances." (emphasis mine)

The purpose being, the tables inside a cluster are co-situated. How can you think the database could make that happen for existing tables, unless of course you drop and re-create them?