Does Swearing invalidate Wudu?

Swearing is not one of the things that invalidate wudu. But it is mustahabb for the one who commits a sin to do wudu , because wudu expiates for sins, as is proven from the Prophet (peace and blessings of Allah be upon him). 

It was mentioned by al-Shirazi in al-Muhadhdhab (2/73) and Ibn Hazm said in al-Muhalla (1/241), narrating from `Aishah, Ibn Mas’ud and others among the Companions  (may Allah be pleased with them), that it is enjoined to do wudu after speaking bad words.  

Al-Nawawi said in al-Majmu’ (2/72): 

“The correct view is that it is mustahabb to do wudu after saying bad words, such as backbiting, malicious gossip, lying, slander, false speech, immoral speech and the like. The purpose of that is expiation for sins, as is proven in the hdiths, but that is not obligatory.”

Ibn al-Mundhir said in his books al-Ishraf and al-Ijma’: 

“The scholars are unanimously agreed that it is not obligatory to do wudu after saying bad words such as backbiting, slander, false speech and the like… al-Shafi’i, Ibn al-Mundhir, al-Bayhaqi and our companions quoted as evidence the hadith of Abu Hurayrah (may Allah be pleased with him), according to which the Prophet (peace and blessings of Allah be upon him) said: “Whoever says in his oath ‘By al-Lat and al-‘Uzza,’ let him say ‘La ilaha ill-Allah,’ and whoever says to another, ‘Come and gamble with me,’ let him give charity.” Narrated by al-Bukhari and Muslim. End quote. i.e., he did not tell him to do wudu.” 

Shaykh al-Islam Ibn Taymiyah said in al-Ikhtiyarat (p. 15): 

“It is mustahabb to do wudu immediately after committing the sin.”

For more, please see these categories: 

Things Which Invalidate the Prayer

Nullifiers of Wudu

 And Allah knows best.