More info: The USDA food pyramid lists peas as part of the protein foods group as well as the fruits and vegetable group. 
How Much Protein Is Needed Per Day?
The amount intake of protein per day is dependent on age, activity level, and sex. Here is look at the daily recommendations from the USDA.
Men: (Ages 19-30): 6 ½ oz. (31-50): 6 oz. (50+): 5 ½ oz.
Women: (Ages 19-30): 5 ½ oz. (31+): 5 oz.
Boys: (9-13): 5 oz. (14-18): 6 oz.
Girls: (9-18): 5 oz.
Children: (4-8): 3-4 oz.
How Much Protein in Peas?
Peas alone would not be sufficient to replace recommended daily protein requirements. At roughly 4 gram of protein per ½ cup of cooked fresh peas, for a woman it would take over 17 cups per day to meet daily requirements. Choosing a varied diet that includes lean meats, dry beans, nuts, eggs, and seeds is a healthy way to get the recommended daily allowance of protein while ingesting many other important nutrients simultaneously.
Nutritional Value of Peas
Peas are a healthy diet choice containing 3.7 grams of dietary fiber per ½ cup fresh cooked, 20% of the RDA for IU vitamin A for women, and 16% of the RDA for folate. 
Other Sources of Protein
Lean Meat: Beef, pork, poultry, ham, lamb, veal, and game meats.
Fish: Finfish such as salmon, cod, and haddock; shellfish including clams, lobster, scallops; canned tuna, anchovies, and sardines.
Non-Meat: Eggs, dry peas, dry beans, nuts, and seeds.