In general, please remember to include your Operating System, the correct answer is often system dependent. Remember that bash is used by default on most Linuxes, OS X and many UNIXes.
Anyway, in your case the OS should be irrelevant, so what you need to do is set the PROMPT_COMMAND variable:
Bash provides an environment variable called PROMPT_COMMAND. The contents of this variable are executed as a regular Bash command just before Bash displays a prompt.
So, since the command you want to run is sourcing
~/.bashrc, add this line to your
. is just an alias to
Now, every time Bash displays a prompt, it will first re-read
~/.bashrc. To get your open terminals (as long as they've been opened after you set
PROMPT_COMMAND) to update just run any command or simply hit Enter.
WARNING: Depending on the complexity of your
~/.bashrc, this could add a noticeable lag since any commands in the file will be executed repeatedly.