Can acne be caused by stress?

No, not directly, but stress can trigger breakouts.

Acne is the result of a combination of factors that lead to blocked pores, some of which are influenced by hormones, such as cortisol and androgens, that are secreted by the endocrine system in response to stress. When stressful situations arise, our adrenal glands stimulate our sebaceous glands (i.e. oil glands) to secrete more sebum (oil). This excess oil leads to, and perpetuates, acne.

Also keep in mind that stress causes increased blood flow and capillary expansion, which makes our skin appear more red and inflamed. Stress can also hinder our absorption of nutrients and thus lead to slower healing due to a weaker immune system.