"A place to call my home" means a place which you can call your home. "A place called my home" is confusing - it's not clear whether "called" means telephoned or given the name of. It also means this has already happened. If you are talking about phone calls, then you would write, "A place from which I can call home." So, you can call home from a telephone in a hotel, for example.

If you need any more help let me know :)

Correction: "A place to call home" This means you have found a new place and that new place will be your home. You feel very comfortable in the new place that you decided to say that:"this is my home". So if I re-worded this for you it would be : " I can say that this place is my new home"