Hola Colin

Not really, no. What we normally say in Spanish literally is: she had the blame/guilt. "La culpa" is a noun (the guilt) but in English the most natural equivalent to this is: she was to blame. Therefore we can't really replace is with the infinitive "culpar" as there's different grammar in the sentences, so it wouldn't work.

However, for a more similar translation in both languages, you could also say:

ella era culpable = she was guilty

In Spanish though, tener la culpa is an idiom that is very commonly used in colloquial Spanish.

Saludos