The different answers you've gotten have slightly different meanings. "I SAW an advertisement about this museum and I WAS curious." (This means that the event happened in the past. In the past, I saw an advertisement, and in the past, I was curious.) "I'VE SEEN an advertisement about this museum and I AM curious." (In the past, I saw an advertisement, and in the present, I am curious. You could also say "I SAW ... and I AM curious." The meaning is essentially the same.) I'm not sure why Rob Pettit changed your phrase to "a museum" instead of "this museum." Both "a" and "this" could be correct, though, depending on the context. You can use "this" if you've already explained what museum you're talking about. It's most correct to use "a" if it's not clear yet what museum you mean. However, in colloquial speech, English speakers do sometimes use "this" as a casual way of introducing a subject, with a similar meaning to "a." I think "this" sounds fine. It's also okay to say "I became curious" or "I got curious," but I think "was" (or "am") sounds better.

It is correct except for one error. The correct sentence should be: "I SAW an advertisement about this museum and I was curious."

"I saw an advertisement about this museum and I got curious"

I've seen an advertisment about a museum and I am curious.

I've seen an advertisment about a museum and I am curious.