The theft took place sometime overnight between Thursday 10th and Friday 11th November at the Copper Kettle Café in Trinity Street, Gainsborough.
Thieves broke in through a door at the back and stole electrical goods, frozen food, a quantity of cash and the two birds.
Café owner David Holmes said: “It’s such a strange thing to steal.”
“We are desperate to get them back and we want anyone with any information to get in touch with the police as soon as possible.”
He added: “I will give a £250 reward to anyone who gives information to the police that leads to a conviction.”
Officers are appealing for anyone who saw any suspicious activity in the area to get in touch as soon as possible, along with anyone who sees, or who is offered the birds for sale.
If you have any information you can call Lincolnshire Police on 101 or call Crimestoppers anonymously on 0800 555 111.