A semiotician is a person who studies signs and how people make meaning with them — adverts, films, clothes, writing, gestures. The word is built in the ordinary way: semiotic + -ian, like musician from music. It names the specialist, not the study; the study is semiotics. You will meet it in academic writing and almost nowhere else. It sounds grand, and it is a little grand. Though actually, a semiotician is not “someone who is semiotic” (that sentence does not mean much). They are someone whose job is to notice what signs are doing. Same Greek root as semiotic: sêma, a sign — still nothing to do with the prefix semi- meaning half.