Tusculan is right. In most jurisdictions in the US, the only requirement for a legally binding contract is that there is an offer, an acceptance and consideration (read: payment). There is no requirement that the contract be memorialized in a writing.
Lawyers/law students will sit around and argue all day about what constitutes “offer,” “acceptance” and “consideration,” but all will agree that a written document is not required for a common-law binding contract to exist.
Proving that an unwritten contract exists may be difficult so a writing may be preferable, but other proof of the contract’s existence can be used (course of dealing, for example).
At common law, certain contracts have to be evidenced by a writing to avoid the statute of frauds. Under the statute of frauds, contracts which are for, among other things, interests in real property (i.e., land), the purchase of goods above $500.00, or contracts that cannot be completed within one year, must all be evidenced by a writing in order to be enforceable by a court.
In addition, under modern law, many types of contracts must be in writing to be considered enforceable under certain regulatory schemes. For example, to have the protection of modern banking/lending laws, a lending contract must be in writing.
Getting back to the OP, if you have saved an electronic version of the contract and the original hard copy is no longer available, such scanned version would likely be considered the “best evidence” of the terms of the contract unless there was some reasonable suspicion that such evidence had been altered and was, therefore, untrustworthy. In such a case, a judge may require that the original be provided.