Synonym for "to Accept Blame"

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.