Is it possible to convert an non-otg port of smartphone to otg port?
Is this for a specific smartphone, or any and all smartphones? 

One potential problem is a USB OTG socket is physically different from a USB device socket, so it might not be able to take an OTG plug.

Also the OTG socket likely offer different electrical capabilities if the smartphone is only a USB device, for example the OTG socket will have the ability to provide power, but a dumb USB device won't.

So, depending on the smartphone, you might make an adapter, carrying an OTG socket, and which would allow you to power the device from an external source.

Further, a USB host-side will have a different set of resistors on the signal wires (compared to a USB device), arranged so that the host side can detect the connection of a USB device. SO the signal 'termination' for the smartphone might not be able to detect a USB device.

Then you'd need to figure out how to have the smartphone drive interrogate the USB device. Which will finally be a software problem, but you will likely need something like root access or a 'jailbrake' to install them.

So it might be easier to make a small adapter which carries a microcontroller, with a USB OTG host to talk to the target USB device, and a USB device to talk to the smartphone's USB socket. 

Edit:
There are a bunch of microcontrollers with both a USB OTG and a USB device, for example some ST Micro STM32's, and they have low-cost developmentboards. I would expect Cypress, who make some easy to use USB-enables MCUs will have parts, but I can't remember. Alternatively, you might even use two USB equipped MCUs.

I would guess that, unless you have a realistic market the cost couldn't be justified. Or, if it's a one off for your own interest, it will be cheaper to get a smartphone with a USB OTG socket first, to do experiments for the overall project, and then investigate the adapter. 

IIRC all Android phones have been fitted with an OTG socket for years (and google will help you find when that change happened)