Veterans' Agricultural Apprenticeship Act of 2017 This bill requires the Department of Agriculture (USDA) to establish a program to make direct loans to farmers and ranchers who will provide mentorship and apprenticeship opportunities for veterans to learn the skills necessary to become successful farmers or ranchers. USDA must carry out the program through agreements with state departments of agriculture that will: select veterans to participate in the program, secure established farmers and ranchers to provide the mentorship and apprenticeship opportunities, and make and administer direct loans to support the resulting mentorship and apprenticeship. The loans must be made without interest and may not exceed a term of one year. Of the amounts appropriated for FY2019-FY2023 for the Office of the Secretary of Agriculture, USDA must use $1 million for each of the fiscal years for the program.