Yes, on the evidence of the earliest Christian writers and of the grave venerated on the Vatican hill. The New Testament never narrates Peter's journey to Rome, but his first letter sends greetings from "Babylon" (1 Peter 5:13), widely understood as an early Christian name for Rome. Writers from the late first century to about 200, among them Clement of Rome, Ignatius of Antioch, Dionysius of Corinth, Irenaeus and Tertullian, point to his ministry and martyrdom in the city.
The evidence that Peter taught and died in Rome comes from those early writers, some by allusion and some in so many words, and from the grave itself. Irenaeus, writing in the late second century, says the Apostles Peter and Paul founded the Church at Rome and entrusted its episcopate to Linus. Benedict XVI noted that Peter ministered first in Jerusalem and then in Antioch before Rome.
For a pilgrim the question has an address. The grave venerated as Peter's lies beneath the high altar of St. Peter's Basilica, in an ancient cemetery excavated in the 1940s. In 1950 Pius XII announced that the tomb of the Apostle had been found, and in 1968 Paul VI said he judged the identification of the relics convincing, while research and debate continue. You can pray above the tomb in the basilica; the excavations beneath it are shown only on guided visits arranged in advance with the basilica.
Christians of other traditions read the same evidence differently, especially on what Peter's presence in Rome means for the papacy. Going there lets you weigh it in the place itself.
Related questions, answered
Does the Bible say Peter went to Rome?
Not in so many words. The Acts of the Apostles does not record it. The main biblical indication is 1 Peter 5:13, written from "Babylon," which is widely understood as a name for Rome. The rest of the evidence comes from Christian writers from the late first century onward.
Source: Catholic Answers: Was Peter in Rome?
Where did Peter serve before Rome?
According to Benedict XVI's summary of the tradition, Peter began his ministry in Jerusalem, was the first bishop of Antioch, and ended his course in Rome as a martyr. The Roman calendar once kept a feast of the Chair of Peter at Antioch.
Source: Benedict XVI: General Audience, 22 February 2006, the Chair of Peter
Was St. Peter the first Pope?
Catholics say yes, because of what Christ gave him. Christ made Simon the rock of his Church, gave him the keys and charged him to feed the flock (Matthew 16:18-19; John 21:15-17), and the Catechism teaches (nos. 881-882) that this office continues in the Bishop of Rome. Other Christians read the same Gospel texts differently.
Source: Catechism of the Catholic Church, nos. 880-882
