We propose a general method to design an arbitrarily shaped radome which can extend the scanning angle of a phased array antenna through finite embedded transformation (FET). The main advantage of our method is that the relationship between the incident angle and steered output angle of the radome can be designed in advance (e.g., a linear relation can be achieved). Unlike a traditional FET, which is often applied onto a slab region, we first apply FET onto an arbitrarily shaped region to bestow the desired radome with an arbitrary shape. Two specific examples have been given to demonstrate our method. Numerical simulations show good performance of our radome.