Can parasites cause sepsis?

Yes and no. If you consider malaria a parasite. If you only consider multicellular organisms to be parasites, then the answer is no - you can be quite ill and die from parasitic burden, but flukes and ringworm cause local inflammation only, and their increase in burden has not been reported to trigger the inflammatory cascade that is present in sepsis and septic shock.
Yes. If you consider symptomatic bacteremia (bacteria in the blood), disseminated infection due to strongyloides stercoralis can cause this as it can transmit colon bacteria into the bloodstream "riding on its back".