Yes, the Holy Father does bless rosaries and other items such as medals at the conclusion of Papal Audiences, the Sunday Angelus, and Papal Masses!
The following is taken from The Pontifical North American College:
At the conclusion of Papal Audiences, the Sunday Angelus, and Papal Masses, the Holy Father gives his Apostolic Blessing. This blessing is for you, your family, your loved ones, and any items for devotional use that you have brought with you to be blessed. Items such as rosaries, crucifixes, holy cards, or medals simply have to be with you to be blessed. The Holy Father has the intention of blessing these articles.
Outside of special papal events such as World Youth Day how can one obtain a rosary or medal blessed by the Pope when one can not be present in Rome?
So what do you do if you want to get a rosary blessed by the pope but can't get to Rome? Anything but buy one already blessed. The best thing to do is talk to a priest or vowed religious you know. Chances are he/she can connect you with someone who is going to Rome or who is currently studying or working there. That person can take your item or obtain one there for you, get it blessed by the pope, and get it back to you. People who travel to Rome are asked to do this all the time. Another option is contacting one of the reputable gift shops in Rome. A decent store near the Vatican will sell you the item, then take it to the next General Audience and have it blessed for no additional charge. - From the Back of the Church