Circular agriculture is an inevitable trend in the sustainable development of global agriculture. At present, there are issues such as insufficient utilization of resources, serious land pollution, and lack of technical support in circular agricultural ecological parks. This study explores the safe application of organic fertilizer to field crops within circular agricultural ecological parks. A peanut (Arachis hypogaea L.)–wheat (Triticum aestivum L.)–maize (Zea mays L.) crop rotation system was selected to research safe application methods of biogas residues on the peanut–wheat–maize crop rotation system. In this experiment, we set up different amounts of biogas residues as the base fertilizers, with no fertilizer and only chemical fertilizer treatments serving as controls. We determined the yield, quality, heavy metal content, and nutrient uptake of wheat, maize, and peanuts, as well as soil nutrient content and heavy metal content under different biogas residue application rates. The results of the experiment are as follows: (1) Biogas residue as a base fertilizer increased the yield of peanuts, wheat, and maize. The highest yield for each crop occurred when the biogas residue amount was 67,500 kg hm−2, with yield increases of 36.7%, 26.6%, and 14.1% for peanuts, wheat, and maize, respectively, compared to the no fertilizer treatment. (2) The application of biogas residue improved the seed quality of peanuts, wheat, and maize. The B3 treatment showed strong quality improvement potential, increasing peanut crude protein content by 3.92–7.48%, soluble sugar content by 36.99–49.70%, crude fat content by 0.95–3.27%, wheat crude protein content by 2.22–8.72%, soluble sugar content by 6.21–8.51%, maize crude protein content by 2.87–3.61%, and soluble sugar content by 21.62–28.05% compared to the control. (3) The application of biogas residue enhanced the uptake of nutrients by crops and increased the contents of effective nutrients in the soil. (4) The application of biogas residue did not cause excessive accumulation of heavy metals in crops and soil. In conclusion, the application of biogas residue positively impacts crop growth, quality, and soil health in circular agricultural ecological parks, and has potential in agricultural production systems. Future research should focus on determining the optimal ratio of organic and chemical fertilizers, their efficient use, and the mechanisms by which organic fertilizer application can increase crop yield and quality, as well as improve soil quality.