At one point in the film, Travis Bickle (played by Robert DeNiro) directly says that he feels isolated and seems to be "God's only man."
This quotation comes from the second act of the film, after Bickle has failed in his attempts to establish a relationship with Betsy (the Cybill Shepherd character). Bickly also fails to convey his sense of growing angst to the Wizard, a fellow cab driver, during this section of the film. Bickle's isolation is again expressed in a voice-over section:
The days go on and on... they don't end. All my life needed was a sense of someplace to go. I don't believe that one should devote his life to morbid self-attention, I believe that one should become a person like other people.
This isolation builds as an inner pressure for Bickle until his character is unable to control his impulses and his rage. Bickle's desire for contact can be seen in his attempts to have a relationship with Betsy and in his attempted confession to the Wizard. We can see this also in the letters he writes to his parents.
However, Bickle's sense of disconnection is also underlined in these episodes. He fails in each effort and cannot bring himself to tell the truth to his parents in his letters. Instead he lies about being a government agent/employee doing secret work.
Perhaps the most poignant symbol of Bickle's disconnection comes in the scenes where he is driving his taxi slowly on the streets of the city at night. He watches crowds on the sidewalks but sits alone with his thoughts in his cab.