Can you get malaria if you get malaria-laden blood splashed onto your scraped-up skin?

Malaria: Because the malaria parasite is found in red blood cells of an infected person, malaria can also be transmitted through blood transfusion, organ transplant, or the shared use of needles or syringes contaminated with blood. Malaria may also be transmitted from a mother to her unborn infant before or during delivery. In your case no because malaria not absorbed through the skin.

Possibly yes: If the blood truly has malaria parasites in it and those parasites get into your system then theoretically yes, it is possible. It is probably much more difficult to get malaria this way than when bitten by a mosquito.