I am currently studying in BTech CSE 2nd year. My maths is very weak and I have to choose the specialization, but I want to choose a career in computer science which does not require maths. If there is maths in any career it should be very little or easy. Please guide me ..
I depends on what you mean by a career. For a low level position with not a lot of chance for advancement it would be possible. But almost all CS fields require some fairly deep understanding of at least some parts of mathematics. As user vonbrand notes it is mostly not calculus, though even that can help.
But one of the big ideas in CS is being able to separate the "simple" algorithms from those that will actually work in practice. You can go a ways with only standard and well known practice, but you won't be in a very good position to make advancements, even in a "career" in programming.
But some parts of CS require more maths than others. User Interface design, for example, and Human Factors, are more concerned with psychology and physiology than maths. But Algorithms, Machine Learning, Operating Systems, and lots of others, depend on being able to think in some of the same ways that a mathematician does. Logical, rather than empirical, evidence, can be fundamental.
The other problem, as you probably already know is that most education programs in CS have quite a lot of required maths. If you don't do well in those courses, your overall record may not be strong enough to advance.
So, perhaps you just need to find a way to deal with learning the maths you need. Tutors can help, especially if they are wise enough to evaluate where your blocks are. Some students need to repeat a lot of things they "should have learned" at an earlier stage, but didn't. A good tutor can help you get past such things, but it might require special insight into learning and into what is most important. But it also takes work (lots of it) on your part.
And, more important than specific mathematical "facts" is a mathematical way of approaching a problem.
If you want a career as a Software Engineer, you can get a passing grade in your math classes, then get a Software Engineering job that doesn't require much math (there are MANY of these available, I had one of these for a few years).
If you really mean you want a career in Computer Science, as in, you want a Ph.D. in Computer Science and a research job in Computer Science then you will likely need to work hard to strengthen your mathematical skills. Many people are not "naturally" good at math, but can do just as good as others by working hard at it. I have several friends like this, who are accomplishing amazing things despite struggling with math early in college.
The fact that you say "BTech CSE" and your name indicates that you are doing a course at an engineering college in India.
Many people in India take such courses to get a career in "Software" which could mean "Software Engineering" or something else. The mathematics requirements for these careers have been mentioned by others.
Many engineering colleges in India teach "standard" calculus as a default math course (since they copy IIT's and the USA) which may not actually be required for every such a career. However, there are many CSE careers which do require a background in calculus.
You should be aware that firms that hire people out of these engineering firms may give some weightage to your grade point score, which will include your score in mathematics courses.
All in all, as said by others, it is best if you take remedial courses so that you can get to a reasonable level in mathematics if you want to pursue a CSE career.