After replacing the battery, the engine will not crank and blinking anti-theft light?

Yep, this is why we use a stay alive battery when we do newer cars because sometimes the security has problems, but if I were you, I would leave the battery disconnected overnight, this should discharge the memory capacitors and allow the system to reboot from the start. Here is a video for next time to show you how the stay alive battery works, and I have left instructions below on how to change out the battery correctly.

https://youtu.be/aCpHCzDjl_w

Also, you can try a hard reboot which is done by removing the negative side of the battery, with the cable loose from the negative side of the battery, hold it to the positive terminal for 1 minute this will discharge the memory capacitors in the BCM and PCM allowing the system to reboot.

Check out the diagrams (below). Please let us know what happens.