The 19-year-old narrowly missed death and sustained a fractured skull from the gunshot.
Doctors said she was beginning to make a good recovery in hospital in London, and her condition is "stable".
She was shot on New Year's Day in a busy street in Walthamstow, in what detectives described as a "cowardly and horrific" attack.
She said: "The person that did this to me must be caught as I would hate to see anyone else suffer the way that I and my family have suffered over this.
"I would urge anyone who has information about this man to contact the police as soon as possible.
"I would never have dreamt that something like this could have happened to me and I am aware that the actions of this man very nearly ended my life.
"I am shocked that anyone would resort to shooting a complete stranger over something as trivial as a mobile phone."
She said she hoped her attacker could be caught before he was given the chance to strike again.
Weapon not found
The woman, from Waltham Forest, east London, was shot in Lea Bridge Road, a busy street, and police believe passers-by may have seen him escaping.
The weapon used was a handgun but police have yet to establish its calibre.
Searches have been carried out in the area but the gun and the bullet have not been found.
Detectives are also keen to speak to the driver of a white Metro-style car seen in the area at the time.
The gunman is described as black, 5 ft 6 ins tall, and was wearing a black skull cap, silver bracelet, dark top and black trousers.
Police are also interested in speaking to the driver of a white Metro-style vehicle seen near the incident.
Gun-murders increasing
Mobile phone theft is an increasing problem for police in London and the phones are the target in more than a third of all street robberies in the capital.
Police have advised mobile users not to make calls in the street.
According to latest figures, the number of gun murders in London has increased by 88%.
In April to November 2001 there were 30, compared with 16 in the same period last year.
Overall, levels of gun crime in the capital are up 20%.
Armed robbery was up 53%, from 435 to 667, meaning at least two people a day were robbed at gunpoint.