The inauguration took place in the capital, Bangui, on Sunday, nearly five months after an alliance of rebel militias toppled the CAR government under the last president.
Djotodia vowed on Sunday "to preserve the peace, to consoldiate national unity [and] to ensure the well-being of the Central African people" before the Constitutional Court.
He later called on opponents of his rule to recognize his "unchallenged legitimacy" as president.
Supporters of ousted President Francois Bozize dismissed Djotodia's inauguration.
"This swearing in in illegitimate because Mr.Djotodia owes his position only to the force of Kalashnikovs and foreign mercenaries," the group Front for the Return of Constitutional Order in Central Africa said in a statement, referring to the violent coup earlier this year.
In March, several thousands fighters from a militia alliance known as Seleka took the capital city, Bangui. Seleka leaders had received positions within the CAR government earlier in the year in a deal with then President Bozize. After he failed to comply with Seleka demands to release political prisoners, the rebel alliance toppled the government.
Shortly after the coup, Djotodia proclaimed himself interim president and vowed to hold elections within three years.
Many of the country's 4.6 million citizens have endured months of unrest, with widespread reports of violent attacks by Seleka members against civilians, including claims of sexual assault and murder. The political instability has also kept the government from helping strengthen its economy and moving toward battling poverty.
Earlier this week, United Nations aid chief Valerie Amos warned the Security Council of the crisis in CAR. The Security Council agreed to aid African Union peacekeeping forces, which are set to triple to more than 3,000 troops. However, Amos stressed that the Security Council must seek other measures to ensure the state does not falter irreversibly.
"The failure to act now could not only prolong and exacerbate the appalling conditions the people of the Central African Republic have had to endure, but could also see the crisis spread beyond its borders and throughout a region already facing enormous challenges," she said.
kms/mkg (AP, AFP, Reuters)