Yes, I think you should put what you've suggested.

As you've said, the número de inscripción de ingresos brutos is distinct from the CUIT (tax identification code), though as far as I can tell not everybody has one (it apparently depends on which tax regime you're in). But I think the translation should be this. "Ingresos brutos" is the name of a provincial (not national) tax in Argentina, which should be called "gross income tax" to distinguish it from income tax, a national tax. It can also be called "turnover tax". And the número de inscripción is the registration number.

"REQUISITOS PROVINCIALES
Una vez realizado que la persona física o jurídica de da de alta en la AFIP y obtiene su CUIT, puede realizar su inscripción en la dirección general de Rentas de la Provincia con sede en la localidad. Con este trámite se obtiene el Número de Inscripción de Ingresos Brutos. Esta inscripción será para poder realizar el pago mensual de Ingresos Brutos, la tasa del impuesto variará según la rama de actividad ejercida."
http://www.uaco.unpa.edu.ar/uaco/www/labempresas/documentos/...

"At a national level, the main taxes levied include: Income Tax, Value Added Tax, Minimum Presumed Income Tax, Excise Tax, Personal Assets Tax, and Taxes on Debits and Credits in Bank Accounts and Other Operations.
At the provincial level, taxes are collected and administered by the provincial revenue agencies working under the respective provincial ministries of economy. The main provincial taxes are Gross Income Tax (or Turnover Tax), Stamp Tax and Real Estate Tax."
[...]
Provincial taxes
Gross income tax
All the provinces and the city of Buenos Aires apply this tax on the gross income earned by all companies engaged in commercial, industrial, agricultural, financial or professional activities.
This tax is levied on each commercial transaction and no fiscal credits are awarded for taxes paid during the preceding periods. The rates depend on the industry and sector, ranging from 1.5% to 5% approximately. The taxes are paid throughout the year with payments made monthly or every two months, varying from province to province. Some primary and industrial activities, however, enjoy certain exemptions."
http://www.investandtrade.org.ar/docs/pdf/The_Tax_System_in_...

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Note added at 2 hrs (2017-07-30 23:35:36 GMT)
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"Gross income tax
Gross income tax is a provincial tax applicable to self-employed individuals on gross earnings. The average tax rate is 4% in the Federal Capital (the city of Buenos Aires), and similar rates are applicable in the different provinces. Professionals who do not perform their activity in the form of a company are exempt from the gross income tax in the city of Buenos Aires. The tax is paid by filing monthly tax returns."
http://taxsummaries.pwc.com/ID/Argentina-Individual-Taxes-on...