What rights did Senator McCarthy abuse?
I assume that you are asking what rights Sen. McCarthy abused that other people were supposed to have. If so, the three most important rights that McCarthy abused were the freedom of speech, the freedom of assembly (both from the First Amendment) and the freedom against self-incrimination (from the Fifth Amendment).
McCarthy abused the first two of these rights by questioning people about their political beliefs and associations. He asked them whether they believed in communist ideas and whether they had associated with communists.
McCarthy abused the right against self-incrimination by trying to force the people to testify against themselves. He required them to answer questions about their own beliefs and associations instead of going out himself and getting evidence about those things.