Can females get an erection?

Yes, females can get an erection. The clitoris is the hemologue of the penis and will become erect when a female is aroused. There are also erectile tissues surrounding the urethra, known as the paraurethral sponge which become engorged in a similar way to a penis during erection.
The clitoris is the homologue of the penis in the female. Clitoral erection is a physiological phenomenon where the clitoris becomes enlarged and firm.