Unless you are a cédula holder, no. That said depending on your area of IT. Always work to be found under the table. Hardware, networking basics, home security. If you are more high level, consider sites like Upwork.com. all you need is a PayPal account and a bank account.
Strange you wouldn't be aware of Upwork???
To correct some language here. To have "regular" employment within a Dominican business corporation, you will need a cédula. There used to be allowances for foreign contractors where the contractor was passed through ITBIS in their payments. Laws to employ foreign contractors have changed.
As i mentioned above, under the table deals are very common if you have basic hardware and networking skills, however i don't really interperet that stuff as "IT", as much as a tech handyman type.
If you have a bank account, PayPal and an account on any contractor website, as I mentioned Upwork.com, you can gain contracts working from basically anywhere. For this, most of those sites require identity verification in your country of origin. This is done by uploading a passport, valid govt id and accompanied by a video interview.
Typical jobs on these sites are cold calling, project management, virtual assistant, and computer programming. Social media types may also find deals there as well.