No, there is no need of degree or any kind of particular background for Salesforce to be a Salesforce developer, but if you will take one or more Salesforce Certifications then it will be a chance to get hired as a Salesforce Developer.
If you have some sort of experience on your resume then also be a chance to get hired, or you have the ability to build solutions/apps for the Salesforce platform.
If you have knowledge of Java programming language and having good command on java then it will be an advantage to get a chance to become Salesforce developer. But it is not necessary that you go and focus on Java.
Any person who has programming knowledge can switch to Salesforce. And if you got knowledge of JavaScript, jQuery, Ajax then it’s an advantage for the current real-time development. If you have to understand the terms, ups, and downs of Salesforce programming then that’s it.