I often work as a contractor and know firsthand how challenging it can be to be accepted into and fit in with an existing team, but it's important that you do.
You want your work experience to be as stress free as possible. You want it to be as comfortable as possible from the standpoint of interacting with the rest of the team. If you want to be effective and productive in your work, then you need to build some amount of goodwill, cooperation, and trust with the rest of the team. You want them to see you as one of them, not as an intruder or as an outsider.
At least some of your work is going to depend on communication, input, and cooperation with and from the rest of the team. In the beginning they may be distrustful of you, they may be resentful of your presence, they may be reticent to engage with you, and some of them may be outwardly hostile to you.
When you speak, always speak in terms of "us and we", "not you and me". You're part of the team and the team is "us and we". Speaking in terms of "you and me" only reinforces the fact that you're an outsider. Find opportunities to engage with the team, but don't be over eager. Be cordial, be professional, be polite, seek opportunities to be helpful, provide input when and if asked. Say "Good Morning" when you come in and say "Good Night" when you leave. Say "Hello" when you pass people in the hallway or in the lunch room.
There's a real balancing act that you'll need to perform over time in order to be accepted as a part of the team, and it may take weeks or even months.
If you think of yourself as "just a contractor" then that's all you'll ever be seen and treated as. You'll likely be frustrated, unfulfilled, lonely, and possibly depressed. Human beings need engagement and acceptance, even in the workplace.
Don't get discouraged. I recently worked as a contractor at a client for 13 months and it took 3 months before people really saw and treated me as a part of the team. Slowly over time I built goodwill, cooperation, and trust, but the first 3 months were a lonely, often frustrating time. Every day I felt like I was walking into the lion's den. Nobody talked to me, nobody engaged with me. Gradually, over time and with some effort on my part, the team accepted me and I was treated like everyone else. I was sought out for input, advice, suggestions, etc. I was invited to status and planning meetings, I was included in lunch and social events, etc. Persevere and you'll get there.