Record linkage is the process of finding matches and linking records from different data sources so that the linked records belong to the same entity. There is an increasing number of applications of record linkage in statistical, health, government and business organisations to link administrative, survey, population census and other files to create a complete set of information for more complete and comprehensive analysis. To make valid inferences using a linked file, it has become increasingly important to have effective and efficient methods for linking data from different sources. Therefore, it becomes necessary to assess the ability of a linking method to achieve high accuracy or to compare between methods with respect to accuracy. This motivates the development of a method for assessing the linking process and facilitating decisions about which linking method is likely to be more accurate for a particular linking task. This paper proposes a Markov Chain based Monte Carlo simulation approach, MaCSim for assessing a linking method and illustrates the utility of the approach using a realistic synthetic dataset received from the Australian Bureau of Statistics to avoid privacy issues associated with using real personal information. A linking method applied by MaCSim is also defined. To assess the defined linking method, correct re-link proportions for each record are calculated using our developed simulation approach. The accuracy is determined for a number of simulated datasets. The analyses indicated promising performance of the proposed method MaCSim of the assessment of accuracy of the linkages. The computational aspects of the methodology are also investigated to assess its feasibility for practical use.