The correct option is
B was raining
In the given sentence, 'woke' indicates that the tense of the sentence is past tense. Thus, the answer must be in the past tense.
Option A is incorrect. 'is raining' is in the present continuous tense and not the past tense. Thus, using it will make the tense of the sentence inconsistent.
Option B is incorrect. 'will rain' is in the simple future tense and not the past tense. Thus, using it will make the tense of the sentence inconsistent.
Option C is correct. 'was raining' is in the past continuous tense. Thus, it is in a form of past tense. It indicates that an activity was happening when the subject woke up at a time in the past. Thus, it fits in the sentence and is correct.
Option D is incorrect. 'would rain' is in the past tense but, 'would' is used to indicates future with respect to past tense. For example, He said he would go tomorrow. Since it simply does not indicate an action of the past, it is incorrect.