DHKP-C said the “act of self-sacrifice” had targeted the US, which the group called “murderer of the people of the world”.
The bomber and a guard were killed in the attack at a side entrance of the heavily guarded compound.
The US has warned its citizens not to visit diplomatic missions in Turkey until further notice.
In an online statement the DHKP-C said: “Our warrior Alisan Sanli carried out an act of self-sacrifice on 1 February 2013, by entering the Ankara embassy of the United States, murderer of the people of the world.”
Turkey and the US have denounced the incident as terrorism.
A number of illegal groups ranging from Kurdish separatists to leftist and Islamist militants have launched attacks in Turkey in recent years.
The US state department said a Turkish woman visiting the embassy had been seriously hurt and several staff members had suffered minor injuries.
The DHKP-C is designated a terrorist organization in the US and Europe.
The extreme-left group has been blamed for a number of attacks since the 1970s, including some on US diplomatic missions.
Turkish police carried out a series of raids on suspected members in January.
The embassy building is heavily protected but the US has had long-standing plans to move its compound elsewhere for security reasons.
It was recently reported to be in the final stages of a deal to choose an alternative location.
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