A master's degree is not required to apply for a Ph.D. at Yale, although some programs give preference to applicants with post-baccalaureate training. Consult your program of interest directly for information on how it evaluates applications.
You will need to provide the following with your application for admission:

A statement of academic purpose. You will find the prompt for the statement of purpose in our Application Question FAQs.
A list of all the prior colleges or universities you have attended, accompanied by unofficial transcripts from each school. Unofficial transcripts should be uploaded with your application. Official or paper transcripts are not needed at this time.
Three letters of recommendation. Enter the names of your recommenders directly in the application, and they will receive a link to upload a letter on your behalf.