Amaranth is a grain (or pseudograin as it’s often referred to), and since grains are off the Paleo menu, that includes amaranth.
Paleo and Grains
Although gluten-free, amaranth still contains some of the other anti-nutrients we tend to avoid, including phytates. To try to minimize the negative effects of phytates, you can soak and sprout the amaranth, like you would other phytate-rich foods, such as beans, but there are still better ways to get your carbs in, if that’s what you’re after. Nutritionally, amaranth does offer a fair amount of micronutrients, but much of that is negated by the phytates, which bind to minerals, preventing them from being absorbed by the body, and often causing digestive issues and inflammation in the process.
Amaranth leaves, on the other hand, are a green vegetable, similar to spinach, that can absolutely be included as part of a Paleo diet. They make for a healthy source of various B vitamins, as well as vitamins A and C. They are also rich in trace minerals, including calcium, iron, potassium, zinc, copper and manganese, without the anti-nutrient content of their seeds.
Mark Sisson explains why amaranth seeds are best avoided in this post.