As of May 7, 2020, according to Tensorflow's Installation page with pip, Python 3.8 is now supported. Python 3.8 support requires TensorFlow 2.2 or later. You should be able to install it normally via pip.
What version of Python is compatible with TensorFlow?
TensorFlow is tested and supported on the following 64-bit systems: Python 3.6–3.9. Ubuntu 16.04 or later. Windows 7 or later (with C++ redistributable)
Which version of Python is best for TensorFlow?
Note: TensorFlow supports Python 3.5, 3.6 and 3.7 on Windows 10. Although TensorFlow 2.1 will be the final version of TensorFlow that will support Python 2 (regardless of OS).