In most cases you can convert a pull-start engine to an electric-start. It specifically depends on the type of engine you have. Looking at your engine and performing a little research will let you know if it is both cost effective and feasible to convert your motor to electric-start.
Pull-start engines are not typically equipped with charging coils to recharge a starting battery. Most engines can have the flywheel and coils necessary added as aftermarket parts. Most manufacturers make kits available for this purpose.
Some older engines, including Tecumseh brand engines, do not have the mounting bosses drilled into the motor that would allow these parts to be added. Remove the flywheel cover from the engine and look for the area where an electric starter should be installed. It should be near the ring gear. If there are not holes through the motor where a starter could be mounted, the conversion is not possible.
For most engines conversion kits are available with everything needed to convert a pull-start engine to a 12-volt electric starter. Engines should be ordered according to the specific model number on your motor's identification plate. Kits typically come with a starter switch, hardware, a charging cord and specific installation instructions along with any other parts your specific make and model will need to complete the conversion.