There doesn't seem to be an API to check the CUDA version. But there is a hacky way, which is to print the shared library dependencies of tensorflow internal library.
python -c 'import tensorflow as tf; print(tf.sysconfig.get_lib() + "/python/_pywrap_tensorflow_internal.so")' | xargs ldd |grep cuda
libcublas.so.10.0 => /usr/local/cuda/lib64/libcublas.so.10.0 (0x00007f398a94e000)
libcusolver.so.10.0 => /usr/local/cuda/lib64/libcusolver.so.10.0 (0x00007f3982267000)
libcudart.so.10.0 => /usr/local/cuda/lib64/libcudart.so.10.0 (0x00007f3981fed000)
https://github.com/tensorflow/tensorflow/issues/10827