Your testimony that you had this telephone call is technically enough evidence to show an oral contract. On the other hand, the buyer's testimony that the call never took place or that you did not come to an agreement is enough evidence to show that there was no contract. The court would choose which interpretation was better.
You would probably need to bolster your testimony with documents. A court would be more likely to find that you came to an agreement if you either sent a confirming letter afterwards or made a contemporaneous note of the transaction.
You do not say what you agreed to do in the contract. Your reference to "purchaser" suggests that you agreed to sell something. You should note that an oral contract for the sale of tangible personal property is valid only if the price is less than $500.00.
You prove an oral agreement by either an admission of the party, witness testimony, written confirmation from the other party. The bottom line is, you need to have evidence that the agreement exists.
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An oral agreement can be established if you have some written confirmation of the agreement.
Absent that, you establish it by putting on testimony, such as your own or some non-party witness that overheard the conversation.
Basically, in the situation you describe, it comes down to who the judge believes more. Any independent evidence you have that supports your version will help you win your case. The same thing goes for the other side.