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It's possible, but a pain to do. You need to write parser that takes the text as input and generates a syntax tree; then you need to simplify constructs (eg. converting loops into goto statements and simplify expressions into single-static assignments that have only 1 operation). Then you need to match all of the patterns in your syntax tree with sequences of instructions on the target machine that perform the same tasks. Finally, you need to select the registers to use for each of those instructions, spilling them onto the stack if necessary.
In short, writing an implementation for eval in C is possible, but a huge amount of work that requires a lot of expertise and knowledge in several fields of computer science. The complexity of writing a compiler is the precise reason why most programming languages are either interpreted or use a virtual machine with a custom bytecode. Tools like clang and llvm make this a lot easier, but those are written in C++, not C.