You can get complete amino acid from a variety of grains and legumes. You do not -need- to eat meat, it's just tasty.
"A complete protein (or whole protein) is a source of protein that contains an adequate proportion of all of the essential amino acids for the dietary needs of humans or other animals.  This does not refer to the protein source only containing all the essential amino acids, but also containing them in complete proportion for use by the human body. A source may contain all essential amino acids, but contain one in lower proportion to the others, making it an incomplete protein. In order to be a complete protein, the source must contain all essential amino acids, and contain them in complete proportion for use by the body."
"Some foods contain all the essential amino acids on their own in a sufficient amount to qualify as a "complete protein". Complete protein foods that also obtain the highest possible PDCAAS score of 1.0 are certain dairy products, egg whites, and soy protein isolate. Other foods, such as amaranth, Aphanizomenon flos-aquae, buckwheat, hempseed, meat, poultry, soybeans, quinoa, seafood, and spirulina also are complete protein foods, but may not obtain a PDCAAS score of 1.0"
All from Wiki :)