If it rains tomorrow, that'll make a full week of rain.
Literal
Tomorrow rain [subject-が] fall-if, full 1-week rain [subject-が] continue [result-ことになる].
~ことになる ('it will amount to, it will turn out that') frames the result as an objective consequence rather than a personal decision. 丸1週間 ('a full week') uses 丸 as a prefix meaning 'entire, complete.' 続く is 'to continue.'