No, RNA does not produce DNA. Instead, DNA is transcribed into RNA, and then RNA is translated into protein. This is the central dogma of molecular biology:

DNA → RNA → Protein

In some cases, RNA can be reverse-transcribed into DNA, but this is not the typical flow of genetic information. Reverse transcription is a process used by some viruses, like HIV, to convert their RNA genome into DNA, which can then be integrated into the host cell’s genome.

Citation: https://www.ncbi.nlm.nih.gov/books/NBK26887/

Portions of DNA Sequence Are Transcribed into RNA

The first step a cell takes in reading out a needed part of its genetic instructions is to copy a particular portion of its DNA nucleotide sequence—a gene—into an RNA nucleotide sequence. The information in RNA, although copied into another chemical form, is still written in essentially the same language as it is in DNA—the language of a nucleotide sequence. Hence the name transcription.

Like DNA, RNA is a linear polymer made of four different types of nucleotide subunits linked together by phosphodiester bonds (Figure 6-4). It differs from DNA chemically in two respects: (1) the nucleotides in RNA are ribonucleotides—that is, they contain the sugar ribose (hence the name ribonucleic acid) rather than deoxyribose; (2) although, like DNA, RNA contains the bases adenine (A), guanine (G), and cytosine (C), it contains the base uracil (U) instead of the thymine (T) in DNA. Since U, like T, can base-pair by hydrogen-bonding with A (Figure 6-5), the complementary base-pairing properties described for DNA in Chapters 4 and 5 apply also to RNA (in RNA, G pairs with C, and A pairs with U). It is not uncommon, however, to find other types of base pairs in RNA: for example, G pairing with U occasionally.