Baby Food Safety Act of 2021 This bill imposes certain safety requirements on infant and toddler food. The bill establishes maximum levels of certain toxic elements (cadmium, and lead, mercury, and inorganic arsenic) allowable in infant and toddler food, defined as food intended to be sold for children up to 36 months old. The Food and Drug Administration (FDA) shall periodically review and, if necessary, further lower these levels. The FDA may also establish limits on other toxic elements upon review of relevant health and dietary data. Furthermore, facilities that manufacture, process, pack, or hold infant and toddler food must have certain controls and plans to ensure that their food complies with the limits on toxic elements established by this bill. Such facilities shall also make publicly available certain information, including results from tests for toxic elements in their infant and toddler foods. The bill also expands the FDA's authority to require a recall of adulterated or misbranded food to include infant and toddler food that exceeds limits on toxic elements. The Centers for Disease Control shall carry out a public awareness campaign about the risks of toxic elements in infant and toddler food. The FDA shall commission research on agricultural methods that minimize levels of toxic heavy metals in crops.