Hi,
I want to develop a game for mobile phones.
I'd like the user to be able to touch and drag the character around.
My question is: Is there a optimal size for the sprite? I'd lik it to be as small as possible but also big enough so it won't be a problem to drag it.

thanks :)

There are no "standard sizes", afaik. Different games have the sprites different sizes, making them different physical sizes on-screen.

Mobile phones also have different screen sizes, and different numbers of pixels per square inch, so 100 pixels high on one screen might be a different physical size than 100 pixels on a different screen.

Maybe consult the design guidelines for iOS and Android.

iOS
"Hit Targets: create controls that measure at least 44 points x 44 points so they can be accurately tapped with a finger."
https://developer.apple.com/design/tips/
Their definition of point: https://developer.apple.com/library/ios/documentation/2DDrawing/Conceptual/DrawingPrintingiOS/GraphicsDrawingOverview/GraphicsDrawingOverview.html#//apple_ref/doc/uid/TP40010156-CH14-SW7

Android
"Touch target size: to ensure balanced information density and usability, touch targets should be at least 48 x 48 dp."
http://www.google.com.br/design/spec/layout/metrics-keylines.html#metrics-keylines-touch-target-size
They speak of "density independent pixels", or "dps": http://www.google.com.br/design/spec/layout/units-measurements.html#units-measurements-density-independent-pixels-dp-

EDIT: Those are the minimum recommended sizes for interactive elements to have on the screen, but the original sprite image can be of any size that's convenient to make and then it's drawn scaled to match the desired on screen size. You can avoid scaling artefacts by using round scale factors: 2x, 3x, 4x etc. (as opposed to some fractional factor like 3.131351).

No standard size, depends on what YOU want but usually a power of 2 (i.e. 16, 32, 64 etc) is the most efficient on the hardware size.