swear: [OE] Swear is a general Germanic word, with relatives in German schwören, Dutch zweren, Swedish svärja, and Danish sverge. They all go back to a prehistoric Germanic *swarjan, a derivative of the base *swar-, which also lies behind the second syllable of English answer. And this in turn may come ultimately from the same Indo-European base as produced English sermon. The verb’s original meaning was ‘take an oath’; its use for ‘curse, blaspheme’ dates from the 15th century. => answer
swear (v.)
Old English swerian "take an oath" (class VI strong verb; past tense swor, past participle sworen), from Proto-Germanic *swarjan-, (cognates: Old Saxon swerian, Old Frisian swera, Old Norse sverja, Danish sverge, Middle Dutch swaren, Old High German swerien, German schwören, Gothic swaren "to swear"), from PIE root *swer- (1) "to speak, talk, say" (cognates: Old Church Slavonic svara "quarrel," Oscan sverrunei "to the speaker").
Also related to the second element in answer. The secondary sense of "use bad language" (early 15c.) developed from the notion of "invoke sacred names." Swear off "desist as with a vow" is from 1898. Swear in "install in office by administration of an oath" is from 1700 in modern use, echoing Old English.