Can you deduct Interest on rental re-fi after a cash purchase?

[Richard Kreder]

I have the opportunity to purchase a property via short-sale, but it requires a cash purchase (won't qualify for mortgage). After I make repairs I would like to finance it and rent it out. 

I believe for rental mortgage interest to be deductible, it must be used for the purchase or improvement to qualify. Has anyone every financed after a cash purchase and is there a provision to do so within a specific time period to make the interest deductible?