Doc's points are well taken and imputation is probably the better approach. But to answer your specific question, you can fit a regression model using pairwise deletion of missing values by first computing the correlation matrix among the model variables and then using the correlation matrix as input to PROC REG rather than the original data. PROC CORR computes the correlation matrix and uses pairwise deletion by default (specify the NOMISS option to use listwise deletion). In the log, REG reminds you that the sample sizes are not equal across the variables, and it then uses the smallest as the sample size for the analysis. Here is an example:
proc corr data=MyData out=CorrMx;
var y x1 x2 x3;
run;
proc reg data=CorrMx;
model y=x1 x2 x3;
run;