You'll have to create a custom circos plot background (in my example GRCm38.cyto) using the length of the miRNAs and predictive genes. Then create a matrix with name_miRNA/start_miRNA/end_miRNA/name_gene/start_gene/end_gene (in my example my_data).

I let you an example with my_data:

Rname   Rstart  Rend    B_Rname B_Rstart    B_Rend
chr12   117525571   117525854   chr6    70844502    70844520
chr6    70769437    70769572    chr6    70844502    70844517
chr6    73225769    73226060    chr6    70844502    70844536
chr7    87284448    87284477    chr6    70844502    70844563

library(RCircos)
data(UCSC.Mouse.GRCm38.CytoBandIdeogram)
GRCm38.cyto <- UCSC.Mouse.GRCm38.CytoBandIdeogram
RCircos.Set.Core.Componentscyto.info=GRCm38.cyto, chr.exclude=NULL, tracks.inside=3, tracks.outside=0)
RCircos.Set.Plot.Area()
RCircos.Chromosome.Ideogram.Plot();
RCircos.Link.Plot(link.data=my_data, track.num=2, by.chromosome=TRUE);

You can use expectation value <=3 to obtain significant miRNA/target pair from psRNAtarget result.

Here, Maximum expectation as explained in psRNAtarget help is as follows:

Expectation value is the penalty for the mismatches between mature small RNA and the target sequence. A higher value indicates less similarity (and possibility) between small RNA and the target candidate. The default penalty rule is set up by the scoring schema. Maximum expectation is the cutoff; any small RNA-target pair with an expectation less than the cutoff will be discarded in the final result. The recommended values are 3.0-5.0 depending on the scoring schema.

And why you are not using Circos tool for representing miRNA and its target? The publication which you have referred, there also they have used circos tool for its representation.