The process is called Direct Consular Filing. Here's what dept. of state says:
"Filing Petitions Abroad - Petitions, Form I-130, which can be filed abroad are limited. Petitions for immediate relative immigrant classifications (see announcement) can be filed abroad by American citizen petitioners who have been authorized to be continuously resident in their consular districts for at least the preceding six months, including members of the U.S. armed forces, emergency cases involving life and death or health and safety, and others determined to be in the national interest. Petitions are filed with USCIS abroad or at the U.S. Embassy or Consulate (when there is no USCIS presence). Refer to U.S. Embassy websites for more information."
http://travel.state.gov/visa/immigrants/immigrants_1340.html
And here's from the U.S. Embassy New Delhi website:
http://newdelhi.usembassy.gov/uscisi130pet.html
Citizenship and Immigration Services
Form I-130 Processing
An immigrant visa is required of anyone who wishes to enter the United States to reside there permanently, whether or not that person plans to seek employment in the United States.
The USCIS Office in New Delhi accepts Form I-130 [Petition for Alien Relative] by U.S. citizens filing for the immigration of their family members classifiable as “immediate relative.”
Immediate Relatives
The following relatives of U.S. citizens are eligible to qualify for immigration in the immediate relative category.
Spouse or Minor Child of a U.S. Citizen An Immigrant Visa may only be processed for a child if he/she has no claim to U.S. citizenship.
Parent of a U.S. Citizen U.S. Citizen must be 21 or over
Step-parent or child of a U.S. Citizen Stepparent-stepchild relationship must occur before the child’s 18th birthday
Note: Grandparents, aunts, uncles, in-laws and cousins cannot sponsor a relative for immigration.
The U.S. Citizenship and Immigration Services at the U.S. Embassy in New Delhi accepts I-130 petitions from U.S. citizens who reside in India. U.S. citizens whose principal residence is not in India, and/or are abroad temporarily as a visitor or on business, must file the petition in the United States.
If you are not eligible to file in New Delhi, you should file the petition with the U.S. Citizenship & Immigration Service Center having jurisdiction over your place of residence or last residence in the United States. Lawful Permanent Residents must file the petition in the United States.
Evidence of Residence
Proof of such residency will include a U.S. passport with an appropriate long-term, valid Indian visa and a Registration Report and Residential Permit issued by the Foreigner’s Regional Registration Office (FRRO) of the Government of India. Additional evidence should include, but is not limited to, on-going employment in India, taxes paid in India, rent/property receipts, and utility receipts in India.
United States Citizens may file their petitions between 09:00 a.m. to 12:00 p.m. on all normal business days i.e. Monday through Thursday. The Petitioners must comply with the filing requirements of this Office.
United States Citizens MUST BE PRESENT to file their petitions. If a United States Citizen is filing for a spouse, it is recommended that the spouse also appear so that immigration officials may ask any questions necessary for the adjudication of the petition.