Because of "was" in the first clause, the second clause also must have a past tense form. The -ing ending is used for present tense forms.
Bobpursley is right -- "was elected"
The correct answer is "was elected" because it is the past tense form of the verb "to elect." In order to determine the correct form of the verb, you need to understand the grammatical rules for forming the past tense. In this case, since the action of being elected occurred before the action of becoming president in 1960, the past tense is appropriate.
