What instrument measures a pulsating current?

By "pulsating" current, I presume you mean alternating current. If so then the answer is YES. Current, (electron flow) is measured with a device called an "amprobe". It measures current flow in amperes. (the device or circuit you're measuring must be in use and drawing power to get a measurement. An amprobe is that electrical meter with a large "clamp" at the top of it. The clamp must be placed around the hot conductor and only one conductor. For example if you put the clamp around a cord running say a toaster, it'll read 0 because the neutral cancels out the signal of the hot conductor. If you're measuring a 3 phase device, you again must measure each of the three "hot" wires individually. The three "legs" should all be close in their amp values. You can average them, but note the highest value is the critical value. Also note that if you look this up on say google, be aware that "Amprobe" is a brand name of the first company who made these devices. (I still have an original from the 70's) Now virtually all electrical meter manufacturers make "amprobes."