Vegetarians often have normal hemoglobin, but low iron stores (ferritin) in liver, muscles and bone marrow. Iron absorption is improved by including Vitamin C (75 mg per meal or about 6 oz orange juice) along with an iron supplement (as much as 50 mg per day) and high iron foods. The ferrous form of iron is more absorbable than ferric.
Unfortunately, iron supplements often cause constipation. To offset that side effect, make sure you eat sufficient fiber (11.5 grams per 1,000 calories consumed) and drink enough water.
Phytates and oxalates can interfere with iron absorption from the gut, but the research is not conclusive on this subject. Phytates are found in bran and whole grains. Oxalates are high in nut and nut butters, beets and beet greens, tea, strawberries, gelatin, rhubarb, spinach, chocolate and wheat bran. Most of these foods are the very substance of a vegetarian diet.
Iron in non-meat foods is called non-heme iron. Vegetarians should eat dark green leafy vegetables, broccoli, legumes, yeast leavened whole grain breads, iron-enriched pasta, rice and cereal and meat analogs which are high in iron. Unfortunately, the iron in these foods is not as absorbable as the iron in meat.
But foods rich in Vitamin C (papaya, orange, cantaloupe, broccoli, brussel sprouts, raw green peppers, grapefruit, strawberries, etc.) can be as effective as meat meals in improving iron absorption. Remember though sunlight and heat destroy that Vitamin C.