Synonym for "to Accept Blame"

Incriminate or inculpate (oneself)

I don't believe there is a single word in English that can meet all of those conditions, but this is the closest thing I can think of. "Incriminate" doesn't necessarily work outside of a legal context, which is why I would generally prefer "inculpate", but I've never actually seen that word used before - it sounds sort of awkward and artificial, even though it isn't too hard to derive by analogy with "exculpate", a word that actually does see ordinary use.

Also, both of these are actions that could be done to someone else; to make it reflexive you'd have to add the prefix "self-", as in "self-incriminate", but this carries the unwanted connotation of accidentally revealing one's involvement in the matter, while your example is clearly looking for a word that indicates deliberate admission of guilt.

All in all, I think you're better off with "accept/admit + [noun]" (blame, responsibility, guilt, culpability, etc.) instead of a single word.

Shoulder perfectly fits here.

Shoulder (verb):
Shoulder the blame, burden, responsibility, cost, etc.
To accept that you are responsible for something bad or difficult

Example: Teachers cannot be expected to shoulder all the blame for poor exam results
[Cambridge English Dictionary]

In your example, you could replace 'accept' with 'shoulder':

By signing the Treaty of Versailles, Germany shouldered the blame for World War I.

It should also insinuate reluctance on behalf of the acceptor.

Acquiesce means to accept reluctantly but it would be strange to use acquiesce in this context because acquiesce does not often have the connotations of blame.

Take the rap (for)

is a colloquial near equivalent, although it has the difference that it suggests that the person admitting guilt may not actually be the culprit, but be protecting someone else.