I doubt that there is a tool at this general level, it is sort of a short circuit to think directly of a prediction tool without looking at the different interaction partners. You should rather specify which type of RNA you are looking at, and sort the problem out biologically for different types of RNAs, as there are many. Also it plays a role, what kind of organism we are talking about. For example: (in animal cells)

• if the RNA is pri-miRNA it might be bound by Pasha and be cleaved by Drosha, binding might depend on pri-miRNA secondary structure (prediction cadidate).
• if the RNA is pre-miRNA or long double stranded RNA it will be cleaved by Dicer
• miRNAs and siRNAs (short dsFragments) will be integrated into the RISC complex
• RISC complex binds messenger-RNA (sequence specific, prediction candidates)
• Proteins like eukaryotic initiation factors (eIF) bind mRNA by recognizing the 5'-cap
• Proteins like poly(A)-binding protein (PAB) bind the ployA tail of mRNA
• etc.

The best prediction candidates are miRNA target prediction and pri-miRNA prediction, in the other cases the proteins bind or interact with RNA no matter what the sequence is. One of many tools to do miRNA target prediction is RNAhybrid. See also this question.

I am dealing with a same problem (lncRNA binding proteins) for quite long time now.
This article is about a machine-learning classifier to predict if lncRNA binds specific protein. So yes, it is possible to predict, but first of all you have to specify the protein. Not much, but so far it's all I've found.
Hope someone knows more.

starBase v2.0 had integrated 111 CLIP-Seq data to decode **protein-ncRNA**, miRNA-lncRNA, miRNA-mRNA, miRNA-circRNA, miRNA-pseudogene, miRNA-sncRNA interactions and ceRNA networks. It includes tens of RNA-binding proteins, including Ago, PRC2 (EZH2), TDP-43, PTB, HuR, FMRP, LIN28, PUM2 etc...

It may help you.

You can use RNAz to find out if the RNA is structured and if the structure is conserved, usually this means that it has some function as an RNA but can be interpreted as bound by an RNA binding protein.