Without explanation, Lewis & Short jumps from
‘to annex by writing, to add to a writing’
to
‘B. Trop. 1. To impute, ascribe, attribute to one the cause of something’.
Etymonline fails at explanation also. How’s ‘write’ semantically related to ‘impute’?
Latin ascribere “to write in, enter in a list; add to in a writing,” figuratively “impute, attribute,”
from ad “to” (see [ad-]) +
scriber “to write” (from PIE root [*skribh-] “to cut”)