This will find all .txt files starting in the current folder (.) and scp them one at a time to hostname and place them in the home folder.

for filename in $( find . -name '*.txt' ); do scp "$filename" hostname:~/ ; done

Edit: It is important to note you want the quotes around the file name incase the filename has a space in it, if it does and you don't quote it then the application will treat it like multiple arguments instead of one.