Healthy Soils Healthy Climate Act of 2020 This bill modifies the Environmental Quality Incentives Program of the Department of Agriculture (USDA) to provide permanent incentive payments to producers to adopt practices designed to improve soil health through increasing carbon levels in soil. USDA must conduct a study regarding changes in soil health and soil organic carbon levels as a result of the adopted practices to improve soil health; develop ranking and scoring criteria under the program that prioritize practices that score highest in soil carbon sequestration on eligible land; create a soil organic carbon conservation activity plan under the program to measure and monitor sequestration and mitigation improvement levels from the practices; provide for streamlined and coordinated procedures for the program and the conservation stewardship program, including contracting, conservation planning, conservation practices, and related administrative procedures; and establish a program to provide grants to land-grant colleges and universities to conduct research relating to soil health and carbon science, and conduct research relating to soil health and carbon science at its agricultural research stations.