Food Sharing Act of 2017 This bill amends the Food and Nutrition Act of 2008 to: (1) reduce from $9 million to $8.5 million the annual limitation on the total amount of grants that the Department of Agriculture (USDA) may provide under the Community Food Projects Competitive Grants Program, and (2) authorize USDA to establish a separate program to provide up to $500,000 annually for grants to establish and carry out gleaning projects. In a gleaning project, an eligible entity: (1) collects edible, surplus food that would be thrown away and distributes the food to agencies or nonprofit organizations that feed the hungry; or (2) harvests for free distribution to the needy, or for donation to agencies or nonprofit organizations for ultimate distribution to the needy, an agricultural crop that has been donated by the owner of the crop. The eligible entities include public food program service providers, tribal organizations, and private nonprofit entities that meet certain requirements for experience, demonstrated competency, cost-sharing, and a willingness to share information regarding the project.