In my first year at the university the first programming course I took was using SICP (that was 1988). However, I had a similar problem like you: for my own computer (actually a Commodore Amiga), there was no Scheme implementation available at that time, only a different Lisp dialect (I don't remember its name).
However, given the flexibility of Lisp, it was pretty simple to "emulate" Scheme syntax just by adding the missing lisp macros and functions in a few scripts. This was actually enough to implement all the exercises from chapter 1 to 3 required during the course (note that SICP does actually not require the full Scheme stack, a small subset is all you need).
So since Clojure is AFAIK a modern Lisp dialect, I guess you could just do something similar, which gives you the fully free choice to write things either in Scheme or Clojure or a mixture of both.
Of course, solving the exercises directly in Clojure will also be possible, both languages are very similar. More important, SICP is not about programming language syntax, it is about the right use of abstractions in programming (for example, with functions, data, and objects). So don't think too much of possible syntax problems, these are not in the focus of this book and most probably of minor concern.