I have two question
Can We use SQL/Oracle Database with Titanium, because our complete business logic is written in Oracle.
How i can use my existing C# code with titanium.
You can use SQLite within Titanium applications, Oracle however is not supported. That doesn't mean you couldn't write your own module though.
If you already have a lot of business logic in C# you should probably look at MonoTouch, otherwise this code can not be used in any way in Titanium.
Hope this helps.
You might be better off using the XHR requests to communicate with a RESTful JSON or XML formatted API endpoint to your databases on your servers.
Any database things you need to store on the device/app itself, as Angus says, can be done with SQLite.