Short answer. Yes, as to a criminal penalty. A witness has the right not to give an answer that will tend to subject them to a penalty for an offense, unless a law provides otherwise — though they generally must still answer other questions, including ones that could establish a civil claim against them.
What the law says
A witness must answer questions, although his or her answer may tend to establish a claim against him or her. However, it is the right of a witness: To be protected from irrelevant, improper, or insulting questions, and from harsh or insulting demeanor; Not to be detained longer than the interests of justice require; Not to be examined except only as to matters pertinent to the issue; Not to give an answer which will tend to subject him or her to a penalty for an offense unless otherwise provided by law
Rule 132, Section 3 — Rights and obligations of a witness. Read the full provision →
The general rule requires answering, even against a civil claim
The rule opens with a broad duty: a witness must answer questions, although his or her answer may tend to establish a claim against him or her. This means the privilege against self-incrimination is narrower than simply avoiding anything unfavorable — a witness cannot refuse to answer merely because the truthful answer would expose them to a purely civil claim.
The privilege applies specifically to criminal penalties
Among the witness's specific rights is not to give an answer which will tend to subject him or her to a penalty for an offense unless otherwise provided by law. This is the actual self-incrimination privilege — it protects against exposure to criminal liability, not against every kind of unfavorable testimony a witness might otherwise be asked to give.
This right sits alongside several other witness protections
The same provision lists other rights in the same breath: to be protected from irrelevant, improper, or insulting questions, and from harsh or insulting demeanor, not to be detained longer than the interests of justice require, and not to be examined except only as to matters pertinent to the issue. The self-incrimination privilege is one protection among several the rule affords a testifying witness.
Why the distinction between civil and criminal exposure matters
A witness weighing whether to answer a difficult question needs to know precisely what kind of exposure the truthful answer creates. If the answer would only support a civil claim against them, the general duty to answer still applies; only where the answer would tend to expose them to a criminal penalty does this specific privilege actually come into play at all.
A witness who wrongly invokes the privilege against a merely civil question can still be compelled by the court to answer it anyway.