Can a Pope declare a dogma?

Yes, the Pope can declare a dogma.  When the Pope speaks ex cathedra (“from the chair”) he is defining something that all Catholics are to believe.  This authority is granted to St. Peter by Jesus in Matthew 16:17-19.
As the Baltimore Catechism states:

Q. 531. What is necessary that the Pope may speak infallibly or ex-cathedra?
A. That the Pope may speak infallibly, or ex-cathedra:
1. He must speak on a subject of faith or morals;
2. He must speak as the Vicar of Christ and to the whole Church;
3. He must indicate by certain words, such as, we define, we proclaim, etc., that he intends to speak infallibly.

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