Yes.
We are Christians…have been since the first century.
First called “the disciples”…
Later called followers of “the way” …and it seems “Nazarenes”
then at Antioch we started being called Christians.
Later in the first century the Church started to be called “Catholic” (see St. Ignatius --again at Antioch --use around the year 100)
So in time Christians began to be also called Catholics.
And as various heresies arose in the first centuries…which claimed to be Christian …the word was used to differentiate Christians from the others was Catholic…
Of course we still called ourselves Christians…but also we used the term Catholic.
Now a days we have many sorts of Christians --who are indeed Christians and our brothers…though we are unhappily not yet in full communion.
Catholics are Christians who in full communion with the successor of Peter. We call our selves Christians all the time…Pope Benedict XVI when addressing the faithful does not usually say “Catholics this or that” but he calls them Christians…for that is what we are.
Other Christians have various degrees of partial communion with us.
Are Catholics Christians??? Yes most certainly! (see my description of myself in the upper right corner)
As one early Christian noted (375AD)
“If you want to know who I am,” he said, “Christian is my name, Catholic is my surname.”
St. Pacian