In order to install Node.js on Raspberry Pi 3, first visit the official node.js site to get the latest node source code for ARM v7. Once you have the link just run the following:

tar -xvf node-v6.10.1-linux-armv7l.tar.xz node-v6.10.1-linux-armv7l/
cd node-v6.10.1-linux-armv7l/
sudo cp -R * /usr/local

You might get errors for copying dangling symlinks (specially for files, bin/node and bin/npm). To solve the issue,

cp --remove-destination bin/node /usr/local/bin/.

Just reboot and start using Node.

Reference: 1. RaspPi Forum 2. Ask Ubuntu

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