The hybrid plant edible grass (Rumex patientia L. × Rumex tianschanicus A. LOS), a member of the Rumex genus, presents a novel food source with a protein content of approximately 30–40%. By incorporating non-traditional feed sources, such as edible grass leaf powder (EGLP), into broiler production, costs could be reduced. The experimental subjects of this study were Arbor Acres (AA) broilers. A total of 300 newly hatched broilers were randomly divided into to five groups, with each group consisting of six cages, housing 10 birds per cage. The control group was fed a basal diet composed of maize and soybean meal. In the experimental groups, varying percentages (3%, 6%, 9%, and 12%) of EGLP were substituted for the corn–soybean meal in the basal diet. In the diet, for days 1–21, the corn content was reduced from 1.90% to 8.20%, and the soybean meal content was lowered from 1.50% to 6.00%. Similarly, in the diet, for days 22–42, the corn content was decreased from 1.17% to 7.00%, while the soybean meal content was reduced by 1.50% to 6.00%. The experiment lasted 42 days and was divided into two phases: the brooding phase (days 1 to 21) and the finishing phase (days 22 to 42). The results show that substituting 3% and 6% EGLP for corn and soybean meal significantly increased the average daily gain (ADG) during the brooding period compared to the control group (p < 0.01). Additionally, the group with a 3% substitution rate exhibited a significant increase in the average daily feed intake (ADFI) during the brooding phase (p < 0.01). Throughout the 42-day experiment, substituting 3% and 6% of EGLP for maize and soybean meal did not significantly affect the overall growth performance of broilers (p > 0.05). However, a 6% supplementation notably reduced the feed conversion ratio (FCR) (p < 0.01). Both the 3% (EG3) EGLP and 6% (EG6) EGLP replacement meals significantly enhanced the antioxidant capacity of broiler chickens, as indicated by the increased levels of the total antioxidant capacity (T-AOC), superoxide dismutase (SOD), and glutathione peroxidase (GSH-Px) (p < 0.01). Additionally, broilers supplemented with 3–12% showed a marked increase in cecal short-chain fatty acids (SCFAs) compared to the control group (p < 0.01). The 3% EGLP replacement diet also significantly boosted the prevalence of Lactobacillus in the cecum (p < 0.01). Furthermore, after EGLP supplementation, there was a higher abundance of SCFA-metabolizing bacteria, particularly Alistipes and Christensenellaceae_R-7, compared to pre-treatment (p < 0.05). The prevalence of Clostridium was significantly greater in the groups receiving 9% and 12% EGLP (p < 0.05), while Butyrivibrio levels were notably higher after supplementation with 12% EGLP (p < 0.05).